Can you talk a player out from leaving on a free transfer?

I have a 21 year old, great player but still have better older options than him. He was complaining he wasn't getting enough first team football so i gave in, and started to play him more regularly but then he got injured and during that injury he complains again about not getting enough games (what can i do he's injured) then he says he's leaving at the end of the season on a free transfer. Can i talk him out of it? i can't even offer him a new contact either.

Try having your captain talk to him. That can help.

With my tactics i was not able to use Sergio busquets (playing as Barca) then he complained in the same way, While i was speaking to him I selected the option, " I am prepared for giving you a place in 1st team, but you should prove yourself on the pitch" and in the same match he got injured and had to be out for 3 weeks. after 4 or 5 days I received a mail saying that Busquets regreted that he argued with me and he is happy again.