The Basque is on the radar of new Barca boss Ernesto Valverde - whom he played for at Athletic Bilbao - who has shown interest in bringing Herrera to the Nou Camp.
The Spanish midfielder has been linked with a return to his homeland, and Valverde has reportedly made Herrera his main transfer target.
Despite the lure of his former manager and one of the few clubs that would be a step up from United, Herrera has no interest of a move to the Catalan giants.
The Bilbao-born playmaker had three seasons with his home town team, the last of which were under Valverde, before he joined United in a £28 million deal in 2014.
United first bid for Herrera the previous season but were rebuffed but, when we came calling again the following year, there was little the club could do.
He has one year left to run on his existing contract, with the option of a further 12 months, but he is likely to be offered a longer-term deal to thwart any potential suitors.
Herrera was voted the club's player of the season after an impressive campaign under Jose Mourinho when he became a key cog in midfield, after the two frustrating seasons of Louis van Gaal's tenure.
He has long been touted as the natural successor to Wayne Rooney as captain and was man of the match in the Europa League final against Ajax.
Herrera's wearing the armband is irrelevant in many respects, though, as he is United's on-field leader and a captain in all but name.
His excellent form also saw him earn a long-coveted senior Spanish cap, when he came on at Wembley against England in November's friendly.
Herrera's work rate, passion, energy and love for the club - a rare thing for a foreign export - has seen him become a fans favourite at United and his stock has risen from outcast to first name on Mourinho's team sheet.
An extremely popular man both on and off the field, he's one of a number of the squad to have raised his game under Jose.
Herrera has answered his manager's wider call for greater leadership and a stronger mentality within the squad.
Turning down Barca and Valverde, who he is known to have a lot of respect for, will only enhance his reputation at United.