Chelsea have submitted their proposal to Tosin Adarabioyo ahead of the summer transfer window.
Adarabioyo will become a free agent at the end of next month.
Newcastle United were previously favourites to sign him but now face stiff competition from the Blues.
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Manchester United are the other club linked with the centre-back but failed to submit an offer for the player.
Adarabioyo made 22 appearances for Fulham this season, scoring twice.
He has spent the last four seasons with Fulham.