The Spurs midfielder is one of several options contacted, alongside reported targets Scott McTominay from Manchester United and Monaco’s Youssouf Fofana.
Hojbjerg is willing to listen to the Cottagers having not started any of Ange Postecoglou’s first three Premier League matches.
Atletico Madrid hope Spurs lower their demands to allow them to enter the race before the transfer window closes at 11pm on Friday night.
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Hojbjerg’s potential exit could allow Postecoglou room to sign a midfield, with Chelsea’s Conor Gallagher among his targets.
Fulham, meanwhile, have rejected an initial £47million bid from Bayern Munich for star midfielder Palhinha. They are holding out for at least £60m and could re-invest the windfall in multiple players.
Palhinha is keen to leave Craven Cottage and has already agreed personal terms with Thomas Tuchel’s German champions.
Wolves have also had a bid rejected for Harrison Reed with Fulham locked in talks to sign Everton’s Alex Iwobi.