Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
Palace boss Ian Holloway is keen to add a striker this week but appears to have lost out to Reading on Sheffield United's Nick Blackman.
The Eagles have also seen an enquiry for Wolves man Sylvan Ebanks-Blake rebuffed so are now set to turn their attention to Russell.
The 22-year-old Scot has 14 goals for the Tannadice club this season and is a Scotland Under 21 international.
But United would sell their prized asset for the right price and Palace could be tempted to act as they look to bolster their bid for promotion to the Premier League.