Porto have a strong negotiating position based on the presence of an €80m ($90.23m) release clause in the 25-year-old's contract but there is some confidence at Spurs that a deal can be done below that figure.
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Tottenham are planning to increase their bid but the clubs remain some way apart in their valuations as negotiations continue, forming one aspect of what promises to be a busy few days at Spurs.
Antonio Conte has stressed the urgency for reinforcements this month rather than waiting until the summer and has identified Diaz, a Colombia international with 16 goals from 26 games across all competitions this season, as a key part of his rebuild.
Spurs are also pursuing an agreement for Adama Traore but there are mixed messages surrounding the prospect of completing a deal. Sources close to Tottenham told ESPN there is some distance left to travel in terms of agreeing a fee -- Wolverhampton Wanderers are believed to want in excess of £20m ($27m) -- but the player is believed to feel a deal is close and Wolves are planning the rest of the season without him.
Spurs are also pushing to sign Franck Kessie, whose deal expires with AC Milan at the end of the season. Sources have told ESPN that Conte is particularly keen to land Kessie this month but Tottenham face competition from Barcelona for his signature.
Should they miss out on Kessie, Spurs will look instead to complete a loan move for Fiorentina midfielder Sofyan Amrabat. Tottenham made contact with the Italian club earlier this week and sources have confirmed reports in Italy that a move will likely contain an option to buy for around €15m.
Tottenham are also considering a move for a defender with Djed Spence, on loan at Nottingham Forest from Middlesbrough, one option under consideration. There are likely to be several outgoings with Tanguy Ndombele, Dele Alli, Giovani Lo Celso and Matt Doherty all available to leave this month.
Lo Celso was left out of Sunday's 2-0 defeat at Chelsea as he searches for a new club while Doherty has been linked with a return to Wolves as part of a deal for Traore.