The England striker is a free agent after turning down a new contract offer from Everton last month.
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TalkSPORT says Sunderland made a move for Calvert-Lewin, but he has resisted their approach - for now.
The centre-forward wants to keep his options at this stage in the window, though favours remaining in the Premier League.
Calvert-Lewin came close to joining Leeds United last month, though his personal demands proved too rich for Elland Road chiefs.