According to Spanish outlet Sport, the newly-crowned La Liga champions are unwilling to meet Man United’s £40 million valuation of the wantaway winder.
Rashford, 27, managed to rediscover so form while on loan at Aston Villa but the club’s failure to secure Champions League football means they won’t be making the move permanent.
The England international is still widely expected to leave Man United this summer following the deterioration of his relationship with Ruben Amorim.
Barcelona are keen on bringing Rashford to Spain but would prefer to offer €5m to €10m for a one-year loan rather than sign him outright.
Liverpool’s Luis Diaz and Arsenal’s Gabriel Martinelli are also options for Hansi Flick’s side as they seek to bolster their attacking line-up.