The Eredivisie champions have reached an agreement with the Red Devils to sell Martinez for a fee which could rise to €55m (£46.6m), and the Argentine has confirmed that he is on his way to Manchester to complete his move.
According to the Daily Mail, Ajax have proposed a deal worth £19m plus add-ons to Rangers for Bassey, while Brighton & Hove Albion have also held talks with the Gers and have tabled a £16m bid.
Meanwhile, a separate report from Sky Sports News claims that Ajax head coach Alfred Schreuder was impressed with Bassey after holding a conversation with the 22-year-old over the phone.
The defender has also attracted interest from clubs in Serie A, the Bundesliga and former Rangers manager Steven Gerrard, who is now in charge of Aston Villa.
Despite interest from a number of clubs across Europe, it is thought that Rangers are relaxed over Bassey's situation, with the Nigeria international under contract at Ibrox until June 2024.
Bassey joined the Glaswegian giants from Leicester City for just £230,000 in the summer of 2020 and he has since developed into an invaluable member of their first-team squad.
The versatile defender, who can play at either centre-back or left-back, made only 15 appearances in his first season at the club, but he elevated his game to new heights in the 2021-22 campaign, starting 45 of his 50 games across all tournaments under Giovanni van Bronckhorst.
Bassey particularly impressed in Rangers' memorable journey to the Europa League final and was named in the competition's Team of the Season.
As a result of Bassey's notable rise over the last 12 months, Rangers now value the Nigerian at £25m and they will not entertain any offers from interested club below their asking price.
Nathan Patterson's £16m departure to Everton last summer is Rangers' club-record sale, while Kieran Tierney's £25m switch from Celtic to Arsenal in 2019 is the all-time record sale in Scotland.
Van Bronckhorst has recently heaped praise on Bassey's development in Glasgow and hopes he can keep hold of the defender this summer.
Speaking to the media, via the Daily Mail, on their pre-season tour, the Dutchman said: "He is fantastic. Bassey is a player who is at the beginning of his career, but also a player who is open to coaching.
"He wants to develop himself, and hopefully we can have him longer here because his development needs to be a couple of years more before he reaches the level that he will be comfortable to get into a new team.
"You never know what will happen. The potential Bassey has is massive, that is potential also other teams will notice he has.
"Calvin came in, he is very sharp, very energetic and happy here. I think it is good for him to keep going, and to give everything he has to this team, which he's done really well so far."
Rangers have already allowed one key player to leave the club this summer, with attacking midfielder Joe Aribo joining Southampton on a permanent deal worth up to £10m.
The long-term future of star striker Alfredo Morelos is also believed to be uncertain as the Colombian has just 12 months remaining on his contract at Ibrox.