Porto have set Tottenham an asking price of £55million for Luis Diaz
Diaz has a release clause of £66m, and it is thought the Portuguese club would be willing to sell for £55m.
But they have turned down Tottenham’s first bid of £37m plus add-ons.
Spurs are determined to get the deal done before the window closes on Monday and are now lining up an improved offer.
However, enticing Diaz to North London could also prove tricky with the winger not interested in the move, according to Record.
Diaz, 25, is one of Europe's most sought-after attackers, having scored 14 goals in 18 league appearances this season, while the Colombian finished joint-top scorer with Lionel Messi at last summer's Copa America.
New Spurs boss Antonio Conte has called for signings before the end of the month.
The club are also in talks with Fiorentina about a loan deal for Moroccan midfielder Sofyan Amrabat.
And they still hope to sign Wolves winger Adama Traore, although the deal has stalled with both clubs wide apart in their valuation.
Wanderers are desperate to keep the Spaniard and Spurs have tried to tempt them by even offering their former defender Matt Doherty in part-exchange.