Reports in Turkey claim that Spurs were one of 12 major European clubs to send scouts to the Champions League Group G match on Wednesday night, which Besiktas won 3-1.
Tosun slammed in his side's second from 25 yards out midway through the first half to cap an impressive display as Besiktas' lone striker in a tough away match.
It is claimed that Tottenham's representative was so impressed that Spurs are now expected to join the bidding for the 26-year-old attacker in the January transfer window.
Crystal Palace were understood to have been chasing Tosun over the summer but their reported £12million bid fell some way short of Besiktas' £18million valuation.
The report states Spurs are prepared to match that fee but how the source knows this from a Spurs scout being present is anyone's guess.
It is most probably an exaggeration in order to give Palace a further nudge while Spurs were most probably there to watch another player anyway - possibly Porto's Ricardo Pereira.