That would require the Hoops getting past NK Maribor into the Champions League proper.
It would be the third season in a row for Mulgrew, but he admits it will never lose its appeal or excitement.
Not even the chastening experience of last season - when they won only one of their six Group games, ended bottom of their section and signed off with a 6-1 demolition in Barcelona - can reduce Mulgrew's enthusiasm to get back to the big boys' table.
It is the belief of the man who will captain the side tonight that it's where Celtic will always want, and need, to be. But Mulgrew does not attempt to underplay the fact the price of failure would be massive.
He said: "Everybody wants to be involved in the Champions League and we will be doing everything we can to get there.
"But Maribor are a good side. They passed the ball well in the second half against us in Slovenia. They have some good players, dangerous players. We will have to be aware of that."
However, Mulgrew is quick to emphasise that Celtic also have great quality in their ranks.
Vitally, they also have experience of how to get past this final hurdle - one which has tripped up Maribor in each of the last two seasons.
"Maribor will be difficult to beat," he continued. "But we have to go out there, be positive and look forward to getting a good result.
"We're on our home pitch. It's where we want to be. The fans get behind us there.
"The stadium is nice and tight and generates a great atmosphere, so it's great to be back at Celtic Park."