Rashford had hoped a permanent move would materialise following his loan spell at the Spanish club last season, but those prospects were thrown into doubt following their signing of Anthony Gordon from Newcastle United.
It remains highly unlikely that Rashford could be reintegrated into the Manchester United squad, and there is a growing acceptance among all parties that a departure remains the best solution.
Barcelona is his preferred landing spot, and sources are suggesting that the player has confidence an agreement still could be reached, even though it would now need to be outside of the £26 million buy clause that was included in last season's loan deal.
Despite their recent deal for Gordon, we understand Barca do continue to admire Rashford and would be happy to sign him if the financial terms suit them.
As such, a £13 million offer is now being mooted in some circles, while we understand the possibility of another loan agreement is also something which is being mentioned.
It is believed Rashford, 28, is calm about the situation. He remains part of Thomas Tuchel's plans for the upcoming World Cup, which keeps his status high - although it does add another layer of complexity to his transfer situation.
Outside of Barcelona, Bayern Munich could yet emerge as a realistic option. Within the Premier League, meanwhile, Chelsea, Arsenal and Tottenham have all been linked with the England international.
At this stage, no formal progress has been made with any of those clubs, but sources suggest each remains a potentially viable destination should Rashford become available later in the summer.
We understand Man Utd would have no issue sanctioning a move to a domestic rival, provided any offer meets their valuation and financial expectations.
United are understood to ideally value Rashford at around £30 million and believe that figure represents a fair price in the current market.