Milner missed Sunday’s 2-0 win over Aston Villa at Anfield after feeling muscle tightness, while Lovren was also out with a knock.
However, both men will be given every chance to prove their fitness prior to Wednesday’s trip to the south coast.
Andy Robertson is expected to be ready for the meeting with Graham Potter’s men after sustaining a minor calf injury against Villa.
The Scot said after that match: "I've just got a bit of a dead calf just in the challenge with Grealish with about 20 mins to go, just a tangle of legs.
“I'll be good to go and hopefully he picks me.”
Xherdan Shaqiri should also keep his place in the squad having brought a lengthy absence necessitated by a muscle issue to an end on Sunday.
Jurgen Klopp is likely to shuffle his pack once again for what is a third game in just six days for the newly crowned champions.
Substitutes at the weekend, Jordan Henderson and Gini Wijnaldum should return to the starting XI on the south coast.
Predicted XI: Alisson, Alexander-Arnold, Gomez, Van Dijk, Robertson, Fabinho, Wijnaldum, Henderson, Salah, Mane, Firmino.