The clubs have been talking all month about a transfer and up until now have failed to meet each other's valuation for the Portugal international.
But Goal says there was a breakthrough in negotiations on Tuesday, with both clubs agreeing on an initial €55m offer.
That total could raise €80m if a number of additional clauses are met, €10 of which should be relatively easy to achieve.
Reports on Tuesday suggested Barcelona were close to hijacking United's move for Fernandes.
However, the attacking midfielder will head to Manchester on Wednesday to complete the switch.