Keylor Navas could move to Manchester United as part of the deal to take David de Gea to Real Madrid
Elsewhere, Arsenal might have been dealt a blow in their pursuit of PSG striker Edinson Cavani.
The Uruguay international, 28, has been strongly linked with the Emirates but Sky Bet have slashed odds to 1/10 that he stays in France.
It comes after a "four-figure sum" was laid on him staying in the French capital.
Gunners boss Arsene Wenger will now have to look elsewhere as he looks to bolster his forward line.
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Moses looked to be on the cusp of a loan move to rivals West Ham but Spurs have entered the race at the 11th hour.
The 24-year-old is expected to sign a long-term contract at Stamford Bridge but will be allowed to leave on loan for the remainder of the current season.
Meanwhile, Spurs boss Mauricio Pochettino remains keen on Southampton midfielder Victor Wanyama but The Daily Mail claim an approach has been blocked.
Wanyama, 24, is keen to leave St Mary's but manager Ronald Koeman is reluctant to sell anymore players.