Moyes wants to add to his options in the final third heading towards next season, with West Ham again looking to challenge at the top end of the Premier League table.
They are also involved in the Europa Conference League, while the five substitutes rule will also come into effect and make greater demands on their squad.
Moyes was left hugely impressed with the impact Lingard had during his loan spell at West Ham and considers him to be a top target.
He also considers Chelsea striker Broja, who caught the eye on loan at Southampton, to be another top target.
Moyes wants both players in through the door, but West Ham face competition.
Lingard is attracting interest from Everton and Tottenham Hotspur, while Broja also has a number of admirers and could yet remain at Chelsea.
West Ham start their preparations for the new season early this month and are due to take on Swiss side Servette in Geneva, before friendlies with Ipswich Town, Boreham Wood, Reading, Rangers, Luton Town and Lens.