Herrera is currently on course to become a free agent at the end of the season when his contract expires and has been heavily linked with Barcelona since Ernesto Valverde, a coach he worked under at former side Athletic Bilbao, took over at Camp Nou last summer.
Herrera was given a 12-month extension to his United deal to prevent it from expiring ahead of this season, but his long-term future has still not been sorted.
A report from ESPN citing 'sources close to United' has claimed that the club remains 'keen to thrash out a deal' with Herrera, while the preference of the player is also to stay.
As things stand, 29-year-old Herrera will become eligible to formally negotiate summer deals with overseas clubs as of January 1st, when he enters the final six months of his current contract unless United have moved to tie him down before then.
Although not always a regular starter, Herrera has been a popular player among United fans ever since he joined the club for around £30m in the summer of 2014.
Injury has resulted in him only starting one game in all competitions so far this season.
Barcelona lightened their midfield during the summer by letting Paulinho, Andre Gomes and Andres Iniesta all leave, bringing in just Arturo Vidal and Arthur. Fringe midfielder Rafinha did return to Camp Nou following a loan spell at Inter, though.