The newly-signed Rangers striker reunites with his former teammate Steven Gerrard at Ibrox.
One of Jermain Defoe's old managers has strongly refuted a claim made by the Rangers striker this week.
But when asked about his interest in the 36-year-old at a press conference on Friday, Hodgson told Football.London: "That's not true. Did people check that?"
When it was reiterated that the claim was made by Defoe himself, Hodgson replied: "Well, it is not true unfortunately. We had no interest in Jermain Defoe.
"He is like a number of strikers, I have seen his name mentioned in relation to the club, but it is one thing people relating their players who are anxious to find a move for to our club, and it is another thing with our club initiating moves to sign a player.
"And I can state, quite categorically, that we made no move at all to sign him. I like Jermain Defoe, I have worked with him and he is a good player and I am pleased he has joined Glasgow Rangers, but we weren't candidates to sign him."
Defoe also claimed it was the lure of another of Hodgson's former England players - Steven Gerrard - that convinced him over a move to Rangers.
The former West Ham United and Tottenham Hotspur player became Gerrard's first January capture, closely followed by the Southampton captain, Steven Davis.
The pair could be joined at Ibrox by the Dundee midfielder, Glen Kamara, and Kilmarnock winger, Jordan Jones - both of whom have agreed pre-contract deals with Rangers.
Will Defoe and Davis be the difference for Rangers in their quest for title number 55?