Rumours have abounded of discord between Rodgers and those higher up at Parkhead, with some even going so far as to say he could leave the club.
This mood was exacerbated by Celtic's failure to qualify for the Champions League, losing to AEK Athens. However, Rodgers has denied any talk of a bad atmosphere.
"We've had a couple of targets we haven't been able to get," he said to 'BT Sport'.
"But I've always had a very, very good relationship with the board and that's the same, even though some people will try to dismantle that.
"We want to improve the team and we've got 'til the end of August to do that. If we don't, I work with the talented players we have here."