A troublesome groin injury brought a premature end to the midfielder's season as he missed out on the closing months of the campaign after an encouraging start to life in Scotland's top tier.
Thistle will return to pre-season training later this month before heading to Spain for a week to gear up for the new Premiership kick-off.
It has been a productive summer so far for manager Archibald, who has already tied down Welsh's midfield counterparts Stuart Bannigan and Gary Fraser on new long-term contracts.
A move for Isaac Osbourne is also under consideration, while the return of Welsh would be another huge boost.
After months on the sidelines, it will take Welsh time to get back up to speed once again.
But Archibald is eager to see the man he appointed his successor as captain 12 months ago back in action.
Archibald said: "It will be like a new signing if we can get Welshy back. He was a huge miss for us and can be a real asset next season.
"He really has got a bit of everything in his game, he is very versatile in the roles he can play, and we did miss him.
"We are desperate to get him back. It has been hard for him, and anyone who has been injured will tell you the same.
"He's had a spell where he was injured all the time and, of course, people will be wondering when he will be fit again.
"As a player, it is horrible when you get tagged with that. We need to get him fit and the club will stand by him and get him as fit as we can and back playing again."