Tottenham have submitted a second bid for Santos left-back Souza.
Standard Sport understands Spurs remained in discussions over a potential deal after an opening bid of around £8million was rejected by the Brazilian side.
The new offer is worth £13m, with the player said to be keen on a move to the Premier League.
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Spurs are in the market for a left-back to provide competition for Destiny Udogie, who has recently returned to training after a hamstring injury.
In Udogie’s absence, responsibilities have largely fallen to right-back Djed Spence to deputise, though 32-year-old Ben Davies filled in for Spurs’ 1-1 draw with Sunderland on Saturday.
Souza, who has a release clause worth €100m (£87.1m) for overseas clubs, is widely regarded at Santos after breaking into the first team last season.
The Brazilian youth international made 24 appearances last term as Santos avoided relegation to the second division.
Thomas Frank has reiterated that Spurs, who are currently 13th in the Premier League table, will be busy in the January transfer window.
Amid talks to sign a left-back, the departure of Brennan Johnson to Crystal Palace and Mohammed Kudus’ thigh injury mean Spurs’ priority for January is attacking reinforcements.
Asked whether he was worried that Spurs’ league position could deter potential targets from signing for the club, Frank dismissed the suggestion and lauded the club’s potential.
“I think we are very attractive in many ways. I think Spurs is a fantastic club with a huge potential,” said Frank.
“I think some of the boxes you need to tick is, of course, the stadium and the training ground and the potential.
“Of course, if we compete against the three teams that are clearly ahead of us - City, Arsenal, and Liverpool, unfortunately - then those three clubs are probably more attractive right now.
“That’s not to say that we can’t attract some of the players that also want to go to those clubs.
“It depends a little bit if there is a spot available for the player to play in those clubs and here, for example.”
