No agreement is in fact in place, and the latest developments suggest the North London side are set to miss out on the prolific young forward.
Nigerian newspaper The Union claim Osimhen has appointed a new agent, based in France, who is in talks with Belgian side Anderlecht over an switch, for the striker who still plays in his homeland.
Anderlecht are determined not to miss out on the forward who netted 10 goals at the tournament in Chile - and cite being beaten to a recent deal by Liverpool as a major reason for this.
Liverpool signed fellow Nigerian prospect Taiwo Awoniyi, a player who Anderlecht were keen on signing, The Union report.
This failure has made them increasingly keen to tie up a deal for Osimhen, although how quickly they will be able to do is another matter, as he is currently on international duty with Nigeria's under-23 side.
Missing out on him would be a disappointment for Spurs, but he is not a player who would be perceived as an instant first team regular, and would have slotted into the under-21 set up instead.
There is still hope of a deal, considering The Mail had reported the club had opened talks over the possibility in early November.
Liverpool's Taiwo Awoniyi is currently on loan at German side Frankfurt, although has played just 18 minutes of first team football there.