Spurs chief Daniel Levy is understood to be a big fan of the Congo international and the club have been tracking the winger since the turn of the year.
Bolasie made a significant impact in the Premier League for Palace last season and, despite interest, manager Alan Pardew is understandably keen to keep him at Selhurst Park.
But what do the statistics say about Tottenham's Bolasie interest?
Having scored just four goals over the last two seasons - including a hat-trick versus Sunderland - Bolasie's goal output will naturally concern Spurs fans. The Congo international - who Palace are unlikely to let leave without a fight - averages 0.1 goals per game, an inferior strike rate to Nacer Chadli, who recorded 0.3 goals per appearance for Tottenham during the previous domestic campaign.
However, while Bolasie's overall campaign appears to lack an end-product at times, it is the way in which he stretches games with pace, tenacity and skill that truly marks his value. He is an accomplished carrier of the ball, as he proved so often last term. Averaging 2.6 dribbles per match, no current Spurs player is comparable in this area - Erik Lamela falls closest behind (1.7).
Bolasie's creative prowess somewhat redeems his lack of goals for the Eagles. With six assists to his name last term, only Lamela (7) and Jason Puncheon (7) set-up a team-mate more often for Spurs or Palace respectively.
Meanwhile, based on his key pass rate per appearance (1.4), the 26-year-old would have ranked third at White Hart Lane upon the conclusion of the most recent campaign. The winger's creativity and ability to stretch the opposition back-line would prove major positives, then. But, for a player of the Congo international's suggested worth, the White Hart Lane faithful are likely to demand more in terms of goals.