But Elland Road sources say Leeds' final offer was £4m with add-ons that fell some way short of Hodgkinson's figure. They also claim Leeds ended talks after a counter offer from Huddersfield.
Speaking to the BBC and Yorkshire Live, Hodgkinson said: “To be honest with you, it wasn’t anything to do with the valuation. The fourth offer we rejected was £13m. The issue was not the valuation, the issue was the structure of the offer, so what I have to consider, having spoken to Lewis, (was) Lewis wanted to play football, that’s what Lewis wants to do, which is fantastic to hear.
Rodrigo makes 'sleeping' Leeds United admission and declares action plan after Whites punishment
Leeds United in ‘talks’ with MLS star as Man Utd eye deal for Whites goalkeeper
Defiant Ralph Hasenhuttl offers Leeds United apology after Southampton score draw
Southampton 2 Leeds United 2: Player ratings as attackers shine but frailties cost Whites
Jesse Marsch reveals extent of Patrick Bamford and Joe Gelhardt's Leeds United injuries
“From my perspective, it’s about how much of that £13m is guaranteed, it’s about how much of it is add-ons and what those add-ons are made up of.
“It’s also about how much cash you’re getting through the door because we were under no illusion and we were looking at replacing Lewis.
“We would have been paying out seven figures, significant seven figures, to replace Lewis, and coming out of Covid we had to make sure the cash we got through the door covered what we had to pay out to replace Lewis.
“So the reality was it wasn’t the amount, £13m was the fourth offer we rejected, it was the structure we rejected."
O'Brien was identified as a player Leeds felt would be suitable for Marcelo Bielsa's style of play but the two clubs could not reach agreement despite investing a significant amount of time in negotiations.
The YEP understands talks were held at ownership level and with no release fee in O'Brien's contract, it simply came down to a matter of valuation for Leeds.
Director of football Victor Orta told the YEP recently it was a common occurence in transfer dealings.
"It was different valuations," he said.
"I respect these kind of things, they happen in football. You have one idea, the club owning the player has another idea. If it matches, perfect, if not they have to continue and you have to continue."
After moving on from the deal, Leeds spent £25m on the deadline day signing of Manchester United winger Daniel James, a long-time target for Bielsa.
As for O'Brien, who scored in a 4-0 win for Carlos Corberan's side last time out, a new deal at The John Smith's Stadium is in the works.