Johnson hinted last week that he wants to play regular first-team football that he is not guaranteed at City, and was left out of the squad for their Premier League opener against Southampton on Sunday.
"Adam is a very good young player who wants to play football," Mancini is quoted as saying on City's official website.
"I understand this so if we can find a solution for him in the next ten days or so, we will.
"It is difficult for him and I understand his situation and are talking to him about it at the moment, but if he stays with us, that is fine, too. We will have to see what happens."
Sunderland are reported to be interested in signing Johnson on a permanent contract.