Shaqiri replaced Keita in the second-half and went on to score twice to give the Reds a 3-1 victory over their arch rivals and lift them back to the top of the Premier League.
The Swiss international will be hoping his performance is enough to earn a starting place in the lineup, although that could mean a switch of formation for manager Jurgen Klopp.
Milner, who missed the game against United, is likely to return to the starting eleven - although he could find himself in the right-back role.
“I just had a bit of a sensation in my hamstring at the end of the Napoli game and made the decision, the manager made the decision [to miss Sunday's game],” Milner said.
“It was the right thing not to risk me at the weekend, so hopefully I'll be fine for the next game.”
Nathaniel Clyne impressed on his first league appearance of the season on Sunday and could be given that mantle once again, however.
Although Klopp has ruled him out of the fixture, he provided a positive update on the youngster's fitness.
“It looks, actually, surprisingly good,” he explained in his pre-match press conference.
“Wolves will still be a bit too early, but after that obviously we can think about him. But for that he needs to train, and so far he didn't train.
“The pain goes down, second by second, which is good.
“The moment he can deal with it then he's on the pitch, and the moment he's on the pitch we will then make the decision. But it looks really good for Trent.”
Wolves, meanwhile, have just one injury absentee in Diogo Jota, who is sidelined for the fixture due to a hamstring strain.
Liverpool: Alisson, Milner, Lovren, Van Dijk, Robertson, Fabinho, Wijnaldum, Shaqiri, Firmino, Mane, Salah.
Wolves: Patricio, Bennett, Coady, Boly, Doherty, Moutinho, Neves, Jonny, Costa, Jimenez, Cavaleiro.