Gordon Smart, editor of the Scottish Sun and former showbiz editor at its London edition, insists his source is an "England player speaking to me direct" and not an intermediary.
Hodgson used a joke about NASA sending a monkey and a human into space in a rocket to illustrate the need for England players to get the ball to Tottenham winger Townsend as quickly as possible during Tuesday's 2-0 win at Wembley.
Townsend has called for an end to the controversy, insisting he took Hodgson's comments as a "compliment", but Smart claims his source says Townsend was offended by Hodgson's words at the time.
Speaking to BBC Radio 5 Live's Sportsweek programme, he said: "He [the source] was angry about Andros Townsend tweeting the following day [to say he was not offended] because he assures me Andros was upset by it."
Smart also claimed a "senior" member of Hodgson's squad as well as coach Gary Neville had to intervene and suggest the manager explain himself more clearly after his first attempt at the joke apparently raised eyebrows among the players.
Explaining the background, he said: "The following morning [after the Poland game] I got call from an England player who wasn't very happy at all about what had gone on in the dressing room.
"I said to the player, 'Do you think this is a good idea to go public? Is there not another way for you to go through with this? Should you not go to the FA about this? Have you spoken to Roy?'
"He said no, he wanted to go public and that he wasn't the only player who was upset. They had agreed they wanted to go public with is.
"I called it in to the office and during the day more than one player did corroborate that Roy had made this remark, that it was taken the wrong way. Across the board everyone did agree it was taken the wrong way.
"I don't for one second think Roy Hodgson is racist. I just think he chose his words really unwisely and misjudged the room.
"As I understood it, it was Roy speaking to Chris Smalling and telling him not to muck about with it and to feed the monkey. There were a few extra words in there that I can't repeat at this time of day on the radio.
"It was taken the wrong way and I know that one senior player and Gary Neville looked at each other and at that point said to Roy: 'I think you better explain what you have just said there'. That was when he explained the NASA anecdote.'
Smart acknowledged his story may cause a rift in the England dressing room but refused to name his source.
"He was an angry guy," said Smart. "When I called him the following day to tell him Roy Hodgson had apologised and had explained the NASA joke, he was even more angry about it then.
"I asked him, 'Would there be an issue in the England dressing room over the next few months?' and he said 'yes'. So it is out in the open and rather this comes out now surely than during the campaign or just before or even after.
"Will [the source's] identity come out? I don't think so because there are four or five potential people who could have said it and I certainly won't reveal my sources.
"For a good 48 hours he really was considering going public and speaking in the first-person about this.
"The backlash was furious and that has probably scared him off. He did say that politically for him it was a real minefield."
Asked if his source was an England player, Smart added: "One hundred per cent direct from the horse's mouth, an England player speaking to me direct."
However, the journalist refused to confirm if his source had taken to the pitch against the Poles.
"I've got to be careful about jigsaw identification," he said.
"If I go in to detail about whether they play or whether they didn't play that would lead to it narrowing it down who it was, so I can't say either way. It's only fair that I protect my source on that."
Former Professional Footballers Association chairman Clarke Carlisle said it would have been better if the source had gone to the FA first.
Speaking on Sportsweek, he said: "If a player has taken offence at something that has gone on during a team-talk in a dressing room, then there are channels for them to go down.
"I think for the player to take it straight to the press instead of reporting it, when we could have had a very efficient investigation, that is the first hurdle where this issue has fallen over."