Danjuma made 34 appearances in all competitions for the Yellow Submarine during the 2021/22 season, scoring 16 goals and laying on four assists.
Lingard, by contrast, had a final season at Old Trafford to forget as he barely started under the management of both Ole Gunnar Solskjaer and Ralf Rangnick.
The England international did enjoy a prolific half season on loan at the London Stadium before that, causing West Ham manager Moyes to lean more towards re-signing the 29-year-old.
The West Ham board, however, view Danjuma, who enjoyed his first season in Spain, as the more favourable signing and are looking to convince the manager to see eye-to-eye with them.
Without major exits thrown into the mix, it seems unlikely that the Hammers can sign both players, primarily due to the high wages that Lingard will command.
Danjuma had the better season of the two, with his performances vital to Villarreal knocking out Juventus and fancied Bayern Munich from the Champions League, before losing in the semi-finals to eventual runners-up Liverpool.
The Dutchman will relish a move back to the Premier League after a largely forgettable spell at Bournemouth in the 2019/20 season when they were relegated.
Newcastle United have also been linked with him.
