The left-back was forced to withdraw from Roy Hodgson's squad on Friday, having picked up what was later confirmed as a minor hamstring strain.
With the problem not as bad as first feared, Everton initially suggested the defender could be in contention to feature against West Ham in the Premier League on Saturday.
While manager Roberto Martinez confirmed Baines was on track with his recovery, the Spaniard said it remained too early to pin down a date for his return to action.
"Scans revealed he had a grade one hamstring injury. Those injuries depend on the individual and how quickly they can heal," he said.
"Leighton is responding well to treatment. It is too early to say how long he is going to be out but we remain very positive."
Martinez also provided an update on Republic of Ireland pair Darron Gibson and James McCarthy - both of whom are injury doubts ahead of Saturday's Premier League clash.
While Gibson played 68 minutes of the defeat to Scotland on Friday before returning to his club, McCarthy withdrew prior to the game sparking a club versus country debate on the midfielder's fitness.
Martinez confirmed Gibson was struggling with soreness in his knee with McCarthy yet to train since leaving the Irish camp on Thursday due to a hamstring problem.
"James hasn't been able to train with the team and that is a worry on a Tuesday leading up to a Saturday game," Martinez added.
"It's a soft tissue injury, like Leighton Baines has, where you need to take it day by day to see how he recovers.
"Darron played against Scotland and got a bit of soreness in his knee.
"He had a long lay-off with his ligament so we need to be cautious but I'm confident he will be available to train very soon."
