The Nerazzurri rate the Argentina international highly and have maintained contact with his representatives, with Sportitalia reporting that Romero would be open to joining Cristian Chivu's side. His profile is understood to have won over both the club's hierarchy and the head coach.
An agreement remains some distance away, however, largely because of the cost of any potential deal. Tottenham are demanding a significant fee for the sale of the former Atalanta man, and Inter Milan have no intention of matching that valuation as things stand.
With plenty of the transfer window still to play out, though, a solution that satisfies all parties cannot be ruled out. The player's own desire to leave Spurs could yet work in Inter's favour as negotiations continue.
Romero has established himself as one of the Premier League's most reliable centre-backs since joining Tottenham, bringing both physicality and composure to the heart of their defence. His experience in Serie A during his time at Atalanta, along with his continental pedigree, makes him an appealing option for Chivu as he looks to strengthen Inter's backline ahead of the new season.
Whether the two clubs can bridge the financial gap remains to be seen, but with the player himself understood to favour a return to Italy, Inter appear to have at least one significant factor working in their favour as the summer progresses.
Tottenham's valuation is understood to sit in the region of €50million, a figure Inter regard as excessive for a defender who has dealt with injury problems in the past.
The club may look to explore alternative structures, such as a loan with an obligation to buy, in order to spread the cost of any deal, though Spurs have shown no sign yet of softening their stance on a straightforward permanent sale, leaving both sides with plenty of work still to do before any agreement can be reached.