Serbia international Vlahovic will have just a year remaining on his contract this summer and Fiorentina are growing frustrated over his demands.
It is believed Vlahovic's agent is pushing for an £6.6m fee to renew the contract, as well as 10 per cent of any future transfer fee.
Commisso says the club hasn't made a decision over the 21-year-old's future, but he has urged Vlahovic to consider who has given him the opportunity to excel in recent seasons.
"We are under active considerations as to what to do," Commisso said.
"He developed here. And he should give recognition, whatever happens, to the club that got him to where he is.
The American owner added: "The more I live here, with this crazy sport, the more I realise how screwed up it is."
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