There has been a host of speculation surrounding the left-back's future in recent weeks, with Arsenal thought to be interested, but it is understood that Brighton have recently been leading the race for the Turkey international.
Kadioglu was in impressive form for his country at Euro 2024, playing every minute of his team's run to the quarter-finals of the competition.
The 24-year-old has been with Fenerbahce since July 2018, meanwhile, making 203 appearances for the club in all competitions, contributing 18 goals and 22 assists.
A recent report claimed that Man United had met with the representatives of the defender to discuss a possible transfer, with Fenerbahce said to be open to a sale despite having him on a contract until June 2026.
Man United 'make bid' for Kadioglu
According to Sporx, Man United have made an official offer for the defender, and the bid is higher than Brighton's when it comes to the initial amount of money.
However, the report claims that Brighton's overall package is worth more, with the Seagulls willing to match Fenerbahce's terms when it comes to add-ons.
Fenerbahce are allegedly expected to reject the two bids from the Premier League duo, but negotiations are set to continue.
The defender has already played four times for his Turkish club this season, scoring once, but he missed the Champions League qualification clash with Lille earlier this week due to a hamstring problem.
Why do Man United want another left-back?
Tyrell Malacia missed the entirety of last season with a serious knee injury, and it remains unclear when the Netherlands international could return, while Man United's first-choice left-back Luke Shaw is facing more time out with a calf issue.
There are concerns when it comes to Shaw's constant muscular problems, and Red Devils head coach Erik ten Hag is thought to be desperate for a new player to arrive in that area of the field before the end of the transfer window.
However, Ten Hag has said that new signing Noussair Mazraoui is capable of providing cover in that area despite being a right-back.
"I think he is a player who is quite difficult to put under pressure. I think especially in English football, that can be very beneficial. There is always pressure on the ball and this is a player who one of his key attributes is that it's very difficult to put him under pressure because he finds often solutions," the Man United boss told reporters on Thursday.
"We can sort problems on the left side with, for instance, Licha [Lisandro] Martinez, with Diogo Dalot, he is capable of playing there. With Mazraoui, we have an additional one who can fill in that position as long as Luke Shaw and Tyrell Malacia are not available."
Man United have also allegedly made a breakthrough in their negotiations with Paris Saint-Germain over a deal for central midfielder Manuel Ugarte.