Spurs sacked Ange Postecoglou on Friday - 16 days after he led them to Europa League success - and quickly set their sights on Frank.
After positive initial talks over the weekend, confidence started to grow on Monday that Frank would be the man to replace Postecoglou, and Tottenham made an official approach to their Premier League rivals later in the day.
Discussions continued into Tuesday and centred on Frank's contract at Brentford, which runs until the summer of 2027 and contains a release clause reported to be in the region of STG10million ($A20m).
Talks have continued into Wednesday, but an agreement between Spurs and Brentford over a compensation package to appoint Frank is close, PA understands.
Further progress is required over Frank's backroom staff and how many will follow the Dane to Tottenham.
The 51-year-old would take over a Spurs side which won the Europa League last month but finished 17th in the Premier League.
One of the first issues he would be faced with, if appointed, concerns the future of captain Son Heung-min, who had a 12-month option in his contract triggered in January.
"I still have one more year left on the contract," Son said on Tuesday, as reported by Korean agency Yonhap. "Rather than saying anything at this moment, I think we should all wait and see what happens."
Meanwhile, Tottenham defender Micky van de Ven has acknowledged it was a "strange" decision to dismiss Postecoglou after the Australian ended the club's 17-year trophy drought.
Van de Ven told Voetbalzone: "That was ultimately a choice from the club.
"We will see what happens now. Of course, we see some rumours about the Brentford head coach, who it will probably be."
On Postecoglou, Van de Ven added: "I think many of the players got along with him well. And of course he is the first coach who has brought success to Spurs in a long time.
"That also shows that he has a certain quality. That also means that he has a winning mentality, 100 per cent. From that, you would of course say that it is strange that he was fired."
