The Hammers, currently just seven points off the bottle of the table, are in desperate need of goals and believe one of the United strikers could make the difference in avoiding a relegation battle.
Chelsea hitman Michy Batshuayi is at the top of the Irons' list of targets, but Slaven Bilic's side have been forced to look elsewhere due to the Blues' reluctance to let the Belgian leave in January.
With both Martial and Rashford having lost their places in the starting XI, and the latter struggling to adapt to life on the wing, West Ham hope that the offer of playing through the middle on a regular basis will be enough to entice one of the players to the London Stadium.