Rashford has subsequently missed a further four Premier League matchday squads and looks set to leave this month with a number of European clubs interested.
Premier League sides, including West Ham, have also posted interest.
AC Milan had been exploring an option to bring Rashford to Italy on a temporary basis for the remainder of the season and now Barcelona are doing the same.
Maynard had on Tuesday has also been been in Italy to hold preliminary talks with Italian giants AC Milan while both West Ham and Tottenham have also expressed interest.
Rashford’s camp and representatives have spoken to Barcelona transfer chiefs with sporting director Deco trying to decide whether a deal is viable.
Read More West Ham join race to sign Man United forward Marcus Rashford but face cost hurdle
Rashford admitted in a bombshell interview last month that he is ready for a ‘new challenge’ and talked about leaving Old Trafford as a ‘when’, not an ‘if’.
Barcelona are reportedly going ‘all out’ to bring Marcus Rashford to the club in the January transfer window
Those clubs plan to hold further meetings with Rashford’s representatives over the coming days.
When asked why he was dropped for the Manchester derby, Amorim said: ‘Selection. We try to evaluate everything: training, performance, game performance, engagement with the team-mates, pushing the team-mates up.
A loan move away from Old Trafford would hinge on what proportion of his wages United are prepared to pay, as well as the size of the fee if there is an obligation to buy.
Rashford has already rejected three offers from Saudi Arabia worth up to £35million-a-year.
Mail Sport previously revealed that Tottenham are among the clubs to hold an interest in Rashford with Spurs keen to bolster their attacking options and rescue their season despite being the second-top scorers in the Premier League.
‘Everything is on the line when we analyse and try to choose the players, so that is my selection.’
One that was performance-related with the suitor paying more based on success and appearances.