Mourinho in Shevchenko challenge
Mourinho (left) wants a lot more from Shevchenko next season
The Ukrainian, 30, scored four Premiership goals in his first season after arriving for £30m from AC Milan.
"Will he be a Chelsea player next season? He has a contract. If he wants to try everything to improve, of course he will," said Mourinho.
"It's up to him, hopefully he is not happy with what he gave to the team, if he's not happy that's a start."
A hernia operation will rule Shevchenko out of the FA Cup final, and Mourinho added: "Sheva's season was not what everyone was thinking, including myself.
"In his defence he has a history of many years in a completely different culture, that can be on his side."
In contrast to Shevchenko, Mourinho was full of praise for his striker partner Didier Drogba.
Drogba scored 32 goals - including 20 in the Premiership - to become the first Chelsea player in 20 years to lift the Golden Boot.
Mourinho said: "He deserves the Golden Boot, to be top scorer in the Premiership without taking penalties is more than deserved.
"Every goal was a proper goal and I am happy for him," added Mourinho, who fears Chelsea's injury crisis will hit their Cup final plans.
Doubts over the fitness of Ricardo Carvalho could leave Chelsea short in the centre of defence.
And Mourinho admitted that after letting William Galls go to Arsenal and Robert Huth quit for Middlesbrough last summer, his team had found themselves short of cover during the season.
"The only thing we can criticise ourselves on is that in the other seasons we had a group of four central defenders," stated Mourinho.
"This season, we had three. A fit Robert Huth this season would have played 35, 40 matches and played an incredible role."
As Mourinho targets Reading's Steve Sidwell, he also hinted that Chelsea's big-spending days could be over.
He said: "There will be no big investments, we won't be involved in the big market."We don't need a lot of players, just a normal season without so many injuries."