Fabian Hurzeler was, noticeably, not specific when talking about his midfielder’s return. But he was upbeat.
Milner picked up an unspecified minor issue in training ahead of the Turf Moor trip.
That would have happened after Hurzeler faced the media on Friday morning.
Milner travelled and was with the squad on matchday as a Mats Wieffer double secured a 2-0 win.
Head coach Hurzeler told BBC Radio Sussex: “He had a small, minor issue in training yesterday (Friday) so we had to take care of him.
“Let’s see how long it will take. I hope not that long.
“I’m quite convinced that we see him back soon.”
Hurzeler recalled Yasin Ayari to his starting line-up rather than Carlos Baleba, whose profile looked the more obvious to replace Milner in a defensive midfield role.
Baleba joined the action late on as substitute for Jack Hinshelwood, at which stage Ayari moved to the No.10 role.
The very last act of the match was Ayari chasing down home goalkeeper Martin Dubravka as he looked to play a pass out of his penalty area.
Although he had not started any of the recent wins, Ayari came into the Burnley game on a high after playing big roles for Sweden as they won two World Cup qualifying play-offs.
Diego Gomez avoided his tenth yellow card of the season so will be available to face Tottenham next Saturday.
Lewis Dunk will remain suspended so early suggestions would be that Hurzeler could go unchanged with his XI.
Eight players have started all five of the recent wins.
Igor Julio offered defensive cover on the bench in the absence of Dunk and, for the far longer term, Adam Webster.