Parkinson has recognised his contribution as Bolton look to steer towards safety in the Championship, although refused to be drawn on what will happen at the end of the season.
Flanagan's deal at Anfield expires in 2019, but Parkinson is only focusing on the present.
“I haven't thought about next season but he's a class act," Parkinson told The Bolton News.
“He epitomises the kind of player who relishes the challenge we are faced with.
“He's played at Premier League level, like Andy Taylor, and they are both absolutely the types we need at the moment.
"He has looked a level above at times. We put him into the team when we went back to a back four.
“I think he could do a job as a wing-back but he's not as dynamic as a Mark Little or Fil Morais.
“Since he has been in the team he's been excellent. He has come on from playing back-to-back games and training well, and that's why we brought him in from Liverpool."