Wilshere has not kicked a ball for the Gunners this season as he continues to battle back to full fitness, though it has been touted that the 24-year-old would still make Hodgson's final squad for the trip to France if he recovers in time.
Dier impressed in Wilshere's absence during the friendly win over France in November, with the 22-year-old Tottenham Hotspur man shielding the back four to great effect to strengthen his chances of being on the plane.
Leicester City man Drinkwater, who has helped the Foxes to the Premier League summit this season, is also in the reckoning and could make his Three Lions debut in tonight's trip to Germany or Tuesday's visit of the Netherlands.
When asked about Dier's defensive midfield qualities, Hodgson told The Telegraph: “He did it against France, that's for sure, and does it for Tottenham. I've been very impressed so have called him up with Drinkwater, who does a similar job for Leicester City.
“They're still in the shadow of Jack Wilshere, who did so well for us before his injury. If all three were available for the Euros, that'd be a nice headache because there might not be space for all three."
Wilshere has impressed in that deep-lying playmaker role in the past for England, but the talented midfielder faces a race against time to recover full fitness in time for France.
Even if he is fit, it remains to be seen if Wilshere will be able to clock up enough Arsenal minutes to get match fit before the season finishes, otherwise Hodgson may elect to keep him at home.