United have had two bids rejected for the England Under-21s right-back with Palace looking for most of the fee up front.
Talks have been held over the past few days and are likely to continue this week before Wan-Bissaka enjoys a break after the European Championships.
The Guardian reports the two clubs will meet on Monday to discuss the deal and a transfer clause involving Wilfried Zaha.

United inserted a sell-on clause in the transfer and could be set for a £15m windfall if Zaha moves on this summer.
The Ivory Coast winger has been linked with both Arsenal and Tottenham in recent times with Palace wanting around £80m.
It is claimed Palace will push to have that clause removed, or at least reduced, when they hold talks with United chief Ed Woodward.
The Eagles want £50m for right-back Wan-Bissaka and the latest offer is believed to have included clauses deemed unrealistic.
Wan-Bissaka is keen to make the switch to Old Trafford but is contracted until 2022 and Palace won't budge on their valuation.
United are likely to turn their attention to a central defender once the deal for Wan-Bissaka is completed.
But they face missing out on Harry Maguire to rivals Manchester City while Matthijs de Ligt is seemingly heading for Juventus .
United have also been frustrated in their pursuit of Issa Diop but could yet revive their interest in Kalidou Koulibaly.


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