The former Liverpool defender, 35, was at Parkhead to watch the 1-1 draw with Leicester City in the International Champions Cup clash, where the visitors emerged triumphant after a 6-5 penalty shoot-out, after having a medical earlier in the day with a year-long deal on the table.
Rodgers, however, said it was unlikely that the former Manchester City and Arsenal centre-back would be in the Celtic squad who will fly out to Kazakhstan on Monday for their Champions League qualifier against Astana
The former Liverpool boss is still working on bringing in another 'wildcard' player who could be in the squad for Kazakhstan.
Speaking about Toure's impending arrival, he said: "It should be complete by tomorrow.
"I brought him into Liverpool to add that bit of experience and help to the centre-halves there at the time and I think you've seen from his impact there and in particular last season, he was a very important player for Jurgen (Klopp) towards the end of the season and played in the Europa League final.
"He was outstanding for me in the big games when I was there.
"He looks after himself, he is a wonderful professional with big experience and I just think with a lot of young players in our squad he can really help them and be of assistance to Scott Brown, who is a wonderful leader.
"It will be nice for Scott to have someone behind him who has that real big-game experience and he could do very well for us.
"I would think that Wednesday would be too soon.
"I would be more looking towards the weekend and some game time against Barcelona to assess where he is at, before the following week
All being well, he will get a good week's training."
Asked if there was a chance to bring a new player in who will go to Astana with his squad, Rodgers said: "That's something that we need to wait and see.
"We have some work going on behind the scenes, hopefully we can get some business done.
"It is going to be tight, it is Saturday evening and we leave Monday afternoon."
Leicester boss Claudio Ranieri was asked again about Riyad Mahrez who has been linked with a £40million move to Arsenal.
The Algeria winger, named man of the match, opened the scoring at the start of the second half with a wonderful curled shot before Celtic's 20-year-old Irish defender Eoghan O'Connell levelled just before the hour mark.
Ranieri, pleased with his players' effort in only their second pre-season match, said: "It is good for you (media) not for us.
"Did you see how Riyad is happy? He played so well, worked so hard for the team, he scored a goal and he stays with us.
"It is very important (to keep him) he is one of our stars.
"Other teams maybe have more stars and maybe he doesn't play at the same level, because maybe is on the bench so it is much better he stays with me."
Asked if Mahrez was worth more than £40million, the Italian said: "Maybe tomorrow some newspapers say £100million, that is good - keep going
It is only speculation."
Source : PA
Source: PA