Milner made his fifth consecutive start, and his third in nine days, as he lined up in midfield for Sunday’s 5-0 victory over United.
After just 26 minutes, Milner pulled up and was forced off the pitch clutching his hamstring, Jones taking his place with Liverpool already 2-0 up.
Klopp’s hand was forced when it came to selecting his midfield for that game, and he was dealt a further blow as Naby Keita was stretchered off following a nasty challenge from Paul Pogba in the second half.
Lijnders spoke to reporters ahead of the League Cup tie at Preston, and though explaining that Keita’s issue was “looking better and better,” he confirmed Milner is likely to miss the next four games.
“Milly, he felt his hamstring getting tight, but then Greenwood went down the line,” he said.
“And how James Milner is – he puts the team always above himself – he went for the sprint, knowing that he wasn’t right, to stop the counter-attack.
“That says a lot about his willpower, it says a lot about how he always puts the team first.
“In that moment, the bigger injury came.
“It looks like he’s out until the next international break, but we spoke already with him and he has a very big role to play.”
“My title is assistant manager, but I think you can give that title to James Milner as well,” the Dutchman continued.
“He is the connection between this playing group [and us] together with Hendo.
“He’s very vocal, very lively and sets the standard. He needs to keep doing that, but he knows that and always does that well.”