The Belgian will continue in goal after Brad Jones picked up an injury in the win against Burnley as the Reds welcome Garry Monk's side to Anfield on Monday
The Liverpool manager dropped Mignolet for an "indefinite" period before the 3-0 defeat at Manchester United a fortnight ago.
But the Belgian made his return as an early substitute in the hard-fought 1-0 victory at Burnley on Boxing Day after his replacement Brad Jones sustained a thigh problem.
Jones' injury means Mignolet, who looked desperately short of confidence at Turf Moor, will regain his starting place for the visit of Rodgers' former club to Anfield.
And the Northern Irishman, who is heavily rumoured to be in the market for a new number one in January, feels the ex-Sunderland stopper can build on his shut-out at Burnley.
"Simon is a resilient character and, like everyone, has taken a wee bit of flak. But to operate at this level you have to deal with that," Rodgers said on Saturday.
"He had a couple of edgy moments yesterday and he will recognise that, but he ended the game with a clean sheet and that will help with his confidence and that as the team."
Rodgers swapped Wales for Merseyside in 2012, and was full of praise for the job done by one of his former players Garry Monk - who took the reins at the Liberty Stadium permanently in May.
Swansea sit eighth in the Premier League - one place above Liverpool - after their 1-0 home win over Aston Villa on Friday, and Rodgers feels Monk has followed the club's recent tradition of playing attractive, free-flowing football superbly.
"It's a very difficult game. I know Swansea very well," he added.
"We had a very good performance against them in the cup [Liverpool beat Swansea 2-1 in the League Cup fourth round in October], at home.
"Garry Monk has done very well. We're in contact fairly regularly and I spoke to him the other day. It's a well-established way of working and way of playing.
"But we now have two games at home after a really good result for us yesterday. We'll arrive into this game and hopefully continue in that mantra and get another three points."
Jones joins a Liverpool injury list that includes long-term absentees Daniel Sturridge (thigh) and Jon Flanagan (knee), as well as Glen Johnson (groin).
It remains to be seen whether Joe Allen will be fit to face his former club after suffering a knock, while Dejan Lovren (groin) is also doubtful.
Monk, meanwhile, looks set to be without Jefferson Montero, who was forced off midway through the first half against Villa due to an apparent hamstring injury.
"We'll have to see about Jefferson. We won't know for the next 24 to 48 hours until we get the scan results," he said on Friday.
"Hopefully it's not too serious because Jeff has been fantastic for us. Coming into a new league, he's been really good. Hopefully he won't be out for too long."