The 32-year-old ended his 12-year association with the Red Devils in July upon the expiration of his contract at Old Trafford.
De Gea kept 190 clean sheets in 545 appearances for Man United across all competitions and won five major trophies including the Premier League, FA Cup, EFL Cup and Europa League.
The Spaniard also received a plethora of individual accolades, being named in the PFA Team of the Year five times as well as winning the Premier League Golden Glove twice, picking up last season's award with 17 clean sheets.
However, De Gea opted to call time on his Man United career this summer as manager Erik ten Hag could not guarantee the goalkeeper regular first-team football, while the Red Devils were allegedly insistent that he would be required to take a significant wage cut.
Man United did not waste time to find a replacement as they swiftly brought in Andre Onana from Inter Milan for around £47m.
De Gea was linked with Bayern Munich, Real Madrid and Inter earlier this summer before all three European giants turned their attention to other targets.
Clubs in Saudi Arabia have also expressed their interest, but De Gea was allegedly not keen on a move to the Middle East in the prime years of his career.
A possible return to his native Spain could be on the cards, though, as Fichajes reports that Real Betis are the frontrunners in the race to sign the former Man United No.1.
Fellow La Liga side Valencia have also been credited with an interest, but Betis are said to be at the front of the queue at present and are waiting for De Gea to respond to their contract offer.
Betis are understood to have identified De Gea as a replacement for 40-year-old former Manchester City shot-stopper Claudio Bravo, who has failed to agree terms over a new contract.
Bravo is yet to play for Betis this season amid uncertainty over his future and will see his current contract expire at the end of the current campaign.
Manuel Pellegrini is short of options in goal at present, as Rui Silva is out with an injury sustained in the heavy 5-0 loss at Barcelona last weekend.
Third-choice goalkeeper Fran Vieites finished the game between the sticks at Camp Nou, and he will likely start for Betis in Thursday's Europa League group-stage opener away against Rangers.