The ex-France international is available on a free transfer this summer, as his contract with Manchester United officially came to an end on June 30.
The speculation linking Como with a switch for the defender has gathered pace in recent days, and according to Fabrizio Romano, a move is now on the verge of going through.
Romano claims that Varane has verbally agreed to join the Serie A outfit, and a deal will be announced once the former Real Madrid centre-back has undergone a medical next week.
The transfer expert claims that Como boss Cesc Fabregas was key in Varane deciding to join the Italian team, who earned promotion from Serie B last term.
Varane featured on 32 occasions for Man United during the 2023-24 campaign, while he represented the Red Devils 95 times in total after arriving from Real Madrid in the summer of 2021.
Monaco 'win' the race for Georgia attacker
Elsewhere, Monaco have allegedly won the race to sign Georgia star Georges Mikautadze, with the Ligue 1 outfit beating a number of clubs to his signature.
The 23-year-old impressed for his country at Euro 2024, scoring three times at the competition, and there has been widespread speculation surrounding his future in recent weeks.
Romano claims that Monaco have now put a deal in place to sign the attacker from Metz, with the club always believed to have been leading the race despite interest from other clubs.
Mikautadze will allegedly cost a €20m (£17.2m) fixed fee plus €4m (£3.5m) add-ons, and he will arrive at Monaco off the back of scoring 13 Ligue 1 goals for Metz in the second half of last season, having returned to the club on loan from Dutch giants Ajax.
Across two spells, the forward made 64 appearances for Les Grenats, scoring 38 goals and registering 13 assists in the process.
Birmingham 'leading' the race for Goldson
Meanwhile, according to Football Insider, Birmingham City are at the head of the queue for Rangers defender Connor Goldson.
The 31-year-old's future has recently been the subject of much speculation, with a number of Saudi Arabian clubs said to be keen on his signature.
However, Birmingham are allegedly leading the race, with the now League One outfit in a strong position to sign him before the end of the transfer window.
Goldson made the move to Rangers from Brighton & Hove Albion in 2018, and he has represented the Scottish outfit on 309 occasions in all competitions.
The centre-back was again an important player for the Gers last season, making 48 appearances in all competitions, but he could leave Ibrox this summer due to the club's financial issues.