The 20-year-old left Ecuadorian side Independiente del Valle to join the Seagulls for just £4.5m, before heading out on loan to Belgium outfit Beerschot for the first half of the 2020-21 campaign.
Caicedo then returned to the Amex Stadium in January and established himself as a first-team regular under Graham Potter, featuring 11 times for the senior side across all competitions.
The deep-lying midfielder started in each of Brighton's final eight Premier League games last season and scored his first top-flight goal in the emphatic 4-0 victory against Man United in May.
According to The Athletic, the Red Devils had the opportunity to sign Caicedo but eventually stepped away from a potential deal, allowing Brighton to swoop in for his signature.
United allegedly identified Caicedo as a possible target in the winter window of 2021, but opted against pursuing their interest further.
Under the tutelage of Ole Gunnar Solskjaer, United instead spent around £37m on Atalanta BC winger Amad Diallo in January 2021, four months after signing midfielder Donny van de Beek from Ajax for around £40m.
Caicedo was a standout performer against United at Old Trafford as Brighton secured a surprise 2-1 victory in their opening Premier League fixture of the new season on Sunday.
The 23-cap Ecuador international, who currently has three years remaining on his contract at the Amex Stadium, will be hoping to cement his place as a regular starter in midfield under Potter following the summer departure of Yves Bissouma to Tottenham Hotspur.
As for United, Erik ten Hag remains on the hunt for a defensive midfielder this summer, with Barcelona's deep-lying playmaker Frenkie de Jong still believed to be his top target.
Despite agreeing a fee in excess of £70m for the 25-year-old last month, negotiations have hit a major stumbling block in recent weeks and Barca president Joan Laporta has recently affirmed that the club intend to keep hold of the Dutchman.
"Frenkie de Jong is a Barca player of great quality and we want him to stay. With him and his teammates, we have a very powerful midfield. He has offers, but we want him to stay and he wants to stay too," Laporta told reporters.
United have also been dealt a blow in their pursuit of PSV Eindhoven's Ibrahim Sangare, who has now put pen to paper on a new five-year contract with the Eredivisie outfit.
However, the Red Devils are allegedly closing in on the signing of Juventus midfielder Adrien Rabiot, with one report claiming that they have reached an agreement in principle to recruit the 27-year-old France international in a deal worth an initial £15m, rising to around £20m with add-ons.
While 10 players have departed Old Trafford so far this summer, Ten Hag has added three new players to his ranks in the form of Tyrell Malacia, Christian Eriksen and Lisandro Martinez.