The Dane, 51, has emerged as a leading contender to replace Postecoglou.
Brentford would be entitled to compensation for Frank, with sources indicating it would cost Tottenham more than £10m to extract him from his contract which runs until 2027.
That figure could rise depending on how many members of staff Frank decides to bring with him if he is named Spurs boss.
Postecoglou was sacked on Friday, 16 days after leading them to victory in the Europa League final, their first major trophy for 17 years.
However, it came towards the end of their worst Premier League season, as they finished 17th after losing 22 of their 38 matches.