West Ham already have enough options in attacking midfield, especially with Manuel Lanzini coming back.
The Hammers have Lanzini, Michail Antonio, Felipe Anderson, Grady Diangana and Marko Arnautovic, who can play out wide.
And the signing of El Shaarawy would only be giving Pellegrini even more of a headache over selection.
West Ham do have a need for additions in January. There has been weaknesses exposed in their squad over the first half of the season.
Pellegrini could do with an injection of quality in central midfield and more depth at full-back.
As a result, spending part of his budget on El Shaarawy would be questionable, and West Ham would be better off focusing their attention on other targets, where additions are more important.