Bailly will leave Man United before the end of the summer transfer window, with the Ivory Coast international not in the plans of Red Devils head coach Erik ten Hag moving forward.
Al-Nassr have been heavily linked with the 29-year-old, who spent last season on loan at Marseille, featuring on 23 occasions in all competitions for the French side, including 17 outings in Ligue 1.
However, according to Sky Sports News reporter Dharmesh Sheth, the Saudi Arabian side's alleged agreement for Laporte means that a switch for Bailly is now unlikely.
Man City have reportedly come to an agreement with Al-Nassr over a fee for Laporte, with the 29-year-old potentially becoming the latest high-profile name to move to the Saudi Pro League.
Sheth claims that Bailly is now exploring other options, with the defender free to leave Old Trafford.
The Ivorian, who started his professional career with Catalan side Espanyol, is said to have received an offer from Besiktas but turned down the chance to move to the Turkish giants.
Bailly's form for Villarreal during the 2015-16 campaign led to Man United signing him in the summer of 2016, and he has represented the 20-time English champions on 113 occasions in all competitions.
The defender's most productive season came in 2016-17, when he made 38 appearances for the Red Devils, but he has struggled with a number of fitness problems since then.
Bailly only made four Premier League appearances for Man United during the 2021-22 campaign, which let to him being allowed to move to Marseille on loan.
The Red Devils released Phil Jones and Axel Tuanzebe earlier this summer, but they are still well-stocked in the middle of their defence, with Harry Maguire now seemingly set to stay at Old Trafford.
Maguire, who is behind Lisandro Martinez, Raphael Varane and Victor Lindelof in the pecking order for the spots in the middle of the defence, has allegedly seen a move to West Ham United break down.
Jonny Evans has also been on a short-term deal at Old Trafford this summer, with Man United still believed to be considering handing the Northern Ireland international a contract until next June.
Ten Hag's side opened their 2023-24 Premier League campaign with a victory on Monday evening, recording a 1-0 win over Wolverhampton Wanderers at Old Trafford.