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Red Devils boss, Erik ten Hag, has made Onana his number-one choice to replace David de Gea, who is now out of contract.
However, United have seen two offers rejected by the Champions League finalists so far for Onana.
The latest bid was worth £38.5 million plus a further £4.2 million in add-ons and bonuses.
The figure Inter are hoping to receive for the 27-year-old is €55m (£47m), and there is an expectation that all parties will reach an agreement in the coming days.
In addition to negotiating with Inter, United have simultaneously been speaking to Onana and have verbally agreed personal terms with the goalkeeper, who is keen to be reunited with Ten Hag at Old Trafford.
