The news is sure to alert a host of clubs in the Premier League and Championship, with the striker proving a hit since his loan move to Swansea in March.
The 20-year-old Italian has scored six goals in eight starts at the Liberty Stadium and helped the Swans into the Championship play-off final.
Loan star: Fabio Borini (right) has helped Swansea to a play-off final
Borini said: 'It is a fact I will leave Chelsea, because I didn't renew the contract.
'I want to carry on playing and I would like to stay in England because it is the best football in Europe.
Feeling Blue: Borini in Chelsea action
'Negotiations went wrong at Chelsea so we both chose to go away and let the contract expire.
'At the end of the season, they will get some compensation for me as a young player.
'But it is too early to think about the transfer window. I think about Wembley now and that is it.'
Swansea are managed by former Chelsea youth-team coach Brendan Rodgers, and Borini seemed to hint at a preference for staying at the club beyond this summer.
He said: 'Brendan has been great and helped me a lot. He just got my confidence higher and higher, which is very important for a young player.
'I have known him since the first day I came to Chelsea. He was impressed by me and I was impressed by him. I knew him a lot from Chelsea and that is the main thing why I came here.
'When the manager knows you already it is a big point to start with. It is a big confidence boost and a big thing for you that a manager is positive about you. He is always available and is a good teacher for football and for life.'
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