Defoe, who won the most recent of his 55 international caps in 2013, has been a key part of Sunderland's successful Premier League survival bid, netting 15 goals in 32 appearances.
The 33-year-old's form has seen him become the third-most prolific English striker in the top flight behind Tottenham's Harry Kane and Premier League Player of the Season Jamie Vardy, both of whom look certain to be in Hodgson's 24-man squad.
But with Manchester United forward Danny Welbeck sidelined for nine months through injury, and Daniel Sturridge short of game time, the door could be open for the former Spurs striker, who is still very keen to represent his country once again.
According to Sky Sports, Defoe said: "If I do go, it'll be a dream because it will be my third tournament and playing for England is something that I've always wanted to do.
"I'm happy with the way I've performed this season. I've ticked every box and if I don't go then I can say at least I've done everything right."
England begin their Euro 2016 campaign against Russia in Marseille on June 11th, before taking on Wales and Slovakia as they look to progress from Group B.