The Catalan outfit were looking at possible loan acquisitions before the deadline, with Fiorentina's Sofyan Amrabat heavily linked with a switch to Camp Nou, but the midfielder ultimately stayed in Italy.
According to ESPN, Xavi's side were also considering Elanga, with the youngster viewed as a player capable of bolstering the team's forward options for the final months of the 2022-23 campaign.
Memphis Depay departed Camp Nou for Atletico Madrid in January, while Ousmane Dembele picked up a thigh problem last weekend that could keep him out for more than one month.
Everton, Borussia Dortmund and PSV Eindhoven were also credited with an interest in Elanga, but the Sweden international ultimately stayed at Old Trafford beyond the deadline.
The 20-year-old has been with Man United since 2014, progressing through the various age groups before making his first-team debut in 2021.
Elanga has made 20 appearances for Erik ten Hag's side this season, including 13 in the Premier League, but he is yet to find the back of the net and has just one assist.
The Swede signed a new deal with the Red Devils in December 2021, with his current terms due to run until the end of the 2025-26 campaign.
As well as Memphis, Barcelona also allowed Hector Bellerin to leave the club in January, with the 27-year-old making the move to Portuguese giants Sporting Lisbon.
Speaking during a press conference on Tuesday afternoon, Barcelona boss Xavi admitted that "replacement signings would be good" for the club before the deadline.
"With the departure of [Gerard] Pique, Memphis and Bellerin, replacement signings would be good for us. In what position? I don't know, it's difficult," the head coach told reporters.
"We are in a situation that depends on 'fair play'. I'm calm about potential signings. Because if one of them arrives today, it is certain that he will not play tomorrow. So I will be more aware of who plays tomorrow."
Barcelona will be looking to make it nine straight wins when they head to Real Betis on Wednesday evening before continuing their league campaign at home to Sevilla on Sunday night.