Football Insider claims the Colombian forward has been identified as a potential replacement for the injured Harry Kane, who is sidelined for the foreseeable future after undergoing surgery.
Spurs are understood to have been monitoring Morelos and could make a move as the transfer window enters its final ten days.
Rangers insisted that no offers for the 23-year-old would be entertained this month, as they view him as vital to their chances of beating Celtic to the Scottish Premiership title.
Morelos has already scored 28 goals this season in all competitions, and hasn't been short of potential suitors.
Spurs' interest comes hot on the news that Internazionale are also keen on the former HJK Helsinki frontman. Jose Mourinho is thought to be keen on bringing in cover for Kane before the end of the month.