The Sunday Express says Beckham, on 97 international caps, was keen to reach 100 and feared that he might miss out if he was unable to impress Steve McClaren on a regular basis.
The newspaper said the midfielder was seeking "crisis talks" with his American club LA Galaxy to discuss a possible return.
But McClaren told BBC Radio Five: "It's not for me to really comment on that. I spoke to David and I've not seen any quotes from him saying that. He has made no indication to me that he intends to do that.
"I can't comment one way or another on the likelihood (of a loan move) ... or how it would benefit one way or another."