It's believed that both clubs will discuss the "finer" details of a transfer that could reportedly cost United up to £50 million.
The Red Devils could sweeten the deal if they're willing to remove or reduce the sell-on clause that was included in the agreement that saw Wilfried Zaha join Palace from United in 2015. Under the clause, United could collect as much as £15 million if Palace decide to sell the Ivorian, according to Fifield.
United's initial offer of about £40 million was rejected, while their second bid has fallen just below the valuation Palace have placed on the England Under-21 international.
There were performance-related incentives included in United's offers - which were believed to include the Red Devils winning the Champions League - that Palace deemed "wildly unrealistic," according to Fifield.
Wan-Bissaka, whose contract at Palace runs until 2022, made 39 appearances in all competitions during his first full season last year.