England head coach Hodgson has named a provisional squad of 26 players for the prestigious international competition.
The former England international has also predicted that one of Jack Wilshere (Arsenal), Jordan Henderson (Liverpool) and Danny Drinkwater (Leicester City) will be omitted from the final 23-man Three Lions' squad.
“Hodgson still has to leave three out and I suspect he will pick just one of Jack Wilshere, Jordan Henderson, or Danny Drinkwater to bring to France,” Shearer wrote on Coral.co.uk.
“I can’t see him taking all three with Henderson and Wilshere having injury concerns. I think the other casualties will be Delph, and of course, Rashford who I mentioned earlier.”
Rashford has had a good season with United and has shown that he is very talented. The 18-year-old forward has scored four goals and has created six chances in 10 Premier League appearances for the Red Devils this campaign.
Delph, who joined City from Aston Villa in the summer of 2015, did not have a good season, and it is a surprise that the midfielder is in the 26-man England squad.
There are fitness concerns over Liverpool midfielder Jordan Henderson, while Arsenal midfielder Jack Wilshere did not play much this season.
Drinkwater has had a good season with Leicester and was a key player in the Foxes’ Premier League title triumph.