The Danish star has been, arguably, the Londoners’ best player since his summer 2013 arrival, with his creativity in midfield having made him a fans’ favourite at White Hart Lane.
His performances are understood to have attracted Italian champions Juventus, who are said to have opened the bidding for him at £16.5m.
However, reports state that this has been knocked back by Tottenham.
But, the Premier League club are believed to have signalled to Juve that an offer of £35m would be acceptable.
Such a move may be designed to scare off the Turin giants and would represent a significant profit on the player Spurs signed for £11.5m in 2013.
It has also been claimed by Gianluca Di Marzio that Juve are looking at another Spurs star, Erik Lamela.