Rodgers has had no complaints with Suarez's attitude since the striker returned from Montevideo, despite Arsenal's bid this week.
"It was a long flight," Rodgers said. "He met up with the others on Sunday and then trained a double session on Monday, did another session on Tuesday and then played some of the game, so he is a wee bit weary.
"He's surrounded by speculation but he is here with us and he is working with the group. He's very much a Liverpool player and in the coming weeks we need to get him up to speed to ensure he's fit and raring to go for the beginning of the season.
"But he said he was OK to be involved. He said he was OK to go on to the pitch and his concentration was fine. The bid may be a distraction but players are paid enough money now to produce for their clubs and he just has to keep his professionalism, which he has done."