Lingard is out of contract at the end of the season and, unless his fortunes drastically improve under new interim manager Ralf Rangnick, the 28-year-old is set to leave United.
West Ham have Nikola Vlasic as a potential replacement for Benrahma when he joins up with Algeria but Moyes is keen to add more firepower.
Depending on when he is released and how far Algeria go in the competition, Benrahma could miss four Premier League fixtures, both legs of the Carabao Cup semi-final — should the Hammers get past Tottenham — and the FA Cup third and fourth rounds.
West Ham boss Moyes, whose side face Brighton on Wednesday night, said: “I think we would like to add but this is where I am hoping that Vlasic will get a bit more prepared and ready for us in that period when he [Benrahma] goes away.
“Nicky is certainly coming much more into our thoughts now and he’s had a good chance to settle in. Said will be a miss for us because he has done an awful lot of good things for us this year, looking more like a Premier League player. Maybe we can add to the front line in some way possible, which might give us other alternatives as well.
“I am hoping that if we don’t get anybody, then Nicky is there as a replacement. We’ll need to be flexible with what we’ve got.”