The Parkhead side don't have their injury issues to seek defensively with Mikael Lustig and Adam Matthews both out of the trip to Leith.
But Mulgrew, who was excellent for Scotland during the midweek victory over Croatia, has welcomed the relentless schedule of games - and wouldn't be looking for a rest in any case.
With one eye on Tuesday's critical Champions League game against Ajax, Lennon, in other cirumstances, may have been tempted to change things around.
Having lost to AC Milan and Barcelona in their opening two games, the Parkhead side now find themselves facing up to a double-header against an Ajax side who have taken one point from their opening two ties.
Essentially, it means that the game against the Dutch side has become a must-win one for Celtic, as Mulgrew appreciates.
However, he would like to get his boots on this weekend before concentrating on Tuesday's meeting.
"I basically had 10 days without any football in the lead-up to the Scotland game so I really don't feel as though I need a break," he said.
"I would always far rather play than not and although it is a huge game for us on Tuesday night, I'd like to play against Hibs as well.
"It is obviously up to the manager what he wants to do and he might wait to see just what shape everyone is in when we all report back from around the world before making his decision.
"But so far as Tuesday's game is concerned, it is the beginning of a big month for us.
"I think we all appreciate just how much hinges on this one for us. We have been really unlucky not to have anything to show from the other games but all that is in the past now. It's what we can do with our remaining games that counts."
Mulgrew himself has matured into one of the main performers for Lennon's side, something that has not gone unnoticed by his manager.
He was the first signing that the Northern Irishman made when he took over at Celtic and the 27-year-old has not disappointed.
"He has been great," said Lennon. "Talk about a multi-functional player and they don't come much better than Charlie.
"You can play him centre-half, central midfield, wide left and left-back. He is a very intelligent player and technically brilliant.
"He has just matured into an all-round very good footballer and we are really pleased with him. He is in a very good place at the minute."
While Mulgrew's versatility has been lauded, the player himself would opt to start in the middle of the park if he was given the choice.
Whether or not that is possible remains to be seen, and his main priority at the minute is that he keeps his place, especially with the lure of Champions League ties.
"I like playing in the middle of the park and I think you see a lot more of the ball there, but to be honest I don't really care where I play. I just want a game," he said.
"It is really difficult to explain what these games mean. The atmosphere is unlike any other game or any other event."
He went on: "The are special nights and I do think that it is a privilege to be involved. It might sound like a cliche but the fans really do give us that something extra.
"Our record at Celtic Park is outstanding and I think that if we could get a result against Ajax then it could kickstart us in the Champions League. You just never know what we could do then in our remaining three games.
"Certainly, there is no-one in our dressing room who has given up hope of getting out of the group."
While Barclona and AC Milan have been regarded by many as the top dogs in the section, there seems to have been a more relaxed view, among fans at least, when it comes to Ajax.
The Dutch champions, however, will still be formidable opponents and Mulgrew has insisted that there is no way they will be taken lightly by anyone in the Hoops dressing room.
In many ways, Celtic finishing third and heading into the Europa League would give them a genuine chance of going deeper into European competition.
Making the last 16 of the Champions League, as they did last season, is an outstanding achievement but for Scottish sides would appear to be the ceiling.
The Europa League would perhaps offer scope to delve further, although Mulgrew is reluctant to look past the forthcoming double-header against Ajax.
"We all know that they are a great side," he said. "There is no doubt that their technical ability will be second to none. There just aren't any so-called weaker teams in the Champions League.
"We know that we'll need to be up for it and we will be. These games are intense. You need to concentrate and you need to focus because you always know that just one mistake can be costly.
"We'll have a good idea of where we are after these two games but our priority is to get the win on Tuesday night."
While Celtic have won plaudits for the manner in which they have competed against AC Milan and Barcelona, the big problem for Lennon's side has been failing to convert their chances.
Mulgrew himself had a glorious chance with a header in the game against Barca that could have changed the course of the tie for the Parkhead side. If they are to take anything from this season's campaign against the best, then they need to be able to put the ball in the net when they chance presents itself.
Georgios Samaras has been outstanding for Celtic at this level in recent seasons but the responsibility has to be shared throughout the team.
"We know that we have to take our chances when we get them," said Mulgrew. "I think we're all aware of that."
Converting them could decide whether or not the passports will go back in the drawer after the festive season.