Hodgson’s current deal is set to expire after France 2016 and the Football Association’s recently-appointed chief executive previously claimed he would not discuss a new contract with the Three Lions manager until after the tournament.
Rumours of a rift between the pair have circulated in recent months, but Glenn has moved to play down any suggestion of this, saying he has discussed the situation amicably with Hodgson.
“I have spoken to Roy,” Glenn said.
“I had a cup of coffee with him, which turned into a few drinks.
“It is a bit of a storm in a teacup. But I spoke to him about it, the position I thought was clear anyway, so yes the air has been cleared.
“Roy is a really good manager… If – and I don’t think it will happen – we had a bad Euros, he would not expect to be kept on. He is a proud man.
“The question for Roy is, how do we set him up to be as successful as we can in the Euros? What can we do? That is what we plan to do.”
England have lost just five games since Hodgson took charge in 2012 and have now won eight and drawn two of their 10 matches since the 2014 World Cup in Brazil. They are currently top of their Euro 2016 qualifying group after six straight wins.
Hodgson’s side continue their qualifying campaign with games against San Marino and Switzerland next month.