Romero, 28, is expected to leave north London this summer after five seasons at the club, with Arsenal among those showing interest alongside Atlético Madrid and Inter Milan.
A source at Spurs has told The Sun the club would not entertain selling to Arsenal under any circumstances, regardless of how open the World Cup finalist is to the move.
Such a switch would be a genuinely eyebrow-raising transfer, echoing Sol Campbell's controversial move from Spurs to Arsenal in 2001, though Campbell left as a free agent, meaning Tottenham had no way of blocking that switch. Romero, by contrast, still has three years left on his contract, leaving Tottenham firmly in control of his future.
Campbell remains the last player to move directly from Spurs to Arsenal, and was branded a "Judas" by fans at White Hart Lane for doing so. Nobody has made the switch since, with William Gallas the last player to go the other way, joining Arsenal from Tottenham at the end of his contract in 2010.
Given that history, and the fierce rivalry between the clubs, Tottenham's stance leaves Arsenal facing an uphill task even if personal terms could be agreed, particularly with manager Roberto De Zerbi already having overseen the arrivals of Jan Paul van Hecke and Marcos Senesi to bolster the position this summer.
Atletico Madrid have since emerged as the clear frontrunners for Romero's signature, having reportedly agreed personal terms with the defender after their move accelerated in recent days, with an initial official bid already rejected by Spurs and a new offer said to be incoming.
Inter Milan's interest has stalled after the Italian club failed to sell centre-back Benjamin Pavard, a departure they needed to fund a move for Romero, leaving Diego Simeone's side to negotiate directly with Tottenham over what is expected to be a fee in the region of €40m.