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Mourinho, who is now in charge of Serie A side Roma, rates Oluwayemi, 20, and frequently included him in first-team training before his sacking last season.
Oluwayemi, who is part of Nigeria’s senior squad, is out of contract at the end of the season and could sign a pre-contract agreement with an overseas club in January.
The former England youth international, who was raised in Essex and qualifies for Nigeria through family, is also attracting interest from Portuguese giants Benfica and a number of German clubs, including Stuttgart.
He came through the ranks at Spurs but could choose to move in the next year to increase his chances of first-team football.
Spurs signed Pierluigi Gollini, 25, on loan in the summer to compete to be the long-term successor to club captain Hugo Lloris, who is out of contract at the end of the season and yet to be offered a new deal by the club.