The Catalan club have been linked with a move for the Argentina international, whose situation at Old Trafford has become increasingly uncertain following a difficult campaign.
Martínez has faced criticism for his performances and was sent off during Manchester United's 2-0 defeat at Chelsea on Saturday. He has also attracted attention after reportedly clashing with the club's hierarchy, while his contract is due to expire at the end of the season. United do, however, hold an option to extend the agreement by a further year.
Barcelona are understood to be considering their defensive options as injuries have affected Hansi Flick's squad. Andreas Christensen, Jules Koundé and Eric García have all been among the players dealing with fitness problems, increasing the need for additional cover.
Flick acknowledged on Friday that the club were assessing the possibility of winter recruitment.
“We always look for what's best for the team. And we're doing that,” he said.
“We'll see, there are still a few weeks until the winter transfer window opens. If we can do something, maybe we will.”
Financial restrictions could complicate any attempt to bring in Martínez or another defender. According to Marca, Barcelona would need to sell a player to create room for a new arrival, with Balde identified as a possible candidate.
The left-back has found opportunities difficult to come by this season, despite the injuries elsewhere in the defence. He has made only three league appearances and has yet to start a match in any competition.
Flick's selection against Alavés was another indication of Balde's current position. Rather than turn to the 23-year-old, the Barcelona coach handed academy midfielder Brian Farinas a senior debut at left-back during the 6-1 victory.
Balde has previously attracted interest from Manchester United, but chose to remain at Barcelona and fight for his place. His situation could now become relevant to United's own recruitment plans, with the Premier League club having experienced problems at left-back.
Luke Shaw's injury record has regularly disrupted his availability, while Diogo Dalot has often been required to cover on the left despite being more naturally suited to the opposite flank.
Balde has made 172 senior appearances for Barcelona and contributed 21 assists. His age and experience make him an attractive option, but any potential departure would depend on the club's willingness to part with a player who has been part of their long-term plans.
For now, Martínez remains a reported target and Balde a possible departure rather than a confirmed transfer plan. Barcelona's financial position and their defensive injury situation could determine whether the speculation develops into concrete business in January.