The pair sustained the injuries in Wasps' European Champions Cup victory over La Rochelle on Sunday with Daly suffering a sprained ankle while No. 8 Hughes damaged knee ligaments.
Daly could be missing for 10-12 weeks while Hughes faces eight to 10 weeks out, British media reported. They were both in Eddie Jones' squad for England's autumn Tests.
"Elliot has injured his ankle - he has a syndesmosis injury - which is pretty common," Wasps Director of Rugby Dai Young was quoted as saying by Sky Sports.
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"He is going to see the specialist to see whether any surgical intervention is required, which depending on the grade of the injury, hopefully it won't be.
"Nathan has an MCL (Medial Collateral Ligament) injury to his knee. Again, we're waiting on the specialist to let us know what's required but we can safely say even the best picture, which is a grade one tear, will require a minimum of four weeks."
Jones also has concerns over the fitness of centre Ben Te'o, lock Maro Itoje and No. 8 Billy Vunipola ahead of the Six Nations which champions England kick off against Italy in Rome on Feb. 4. Their final game is at home to Ireland on March 17.
Hughes could be fit to face Scotland on Feb. 24, while Daly's might be ready tom return against France on March 10.
(Writing by Ken Ferris; Editing by Frank Pingue)
