Wright-Phillips is expected to start in the Europa League round of 32 first leg against Aris Salonika on Tuesday night.
He impressed Mancini when he came on in the second half of the 2-1 derby defeat by Manchester United on Saturday.
With Adam Johnson injured, Wright-Phillips looks to have been given a second chance after handing in a transfer request that was rejected.
Mancini said: "When Shaun played in the second half he played very well and was very important to us.
"I said 20 days ago when we lost Adam Johnson that we could have a problem, because he could have changed this game.
"But we don't have him in this moment and it is maybe important that Shaun can play now."