The 33-year-old car salesman posted a video on Instagram dismissing claims that he and the 43-year-old reality star have reconciled and distancing himself from Price.
Woods said in the video: "I’ve just seen the latest story so I just wanted to come on here and clear it up.
"Engagement ring on, engagement ring off, it’s all bulls***. It’s so muggy, the stories are muggy as well."
He went on: "I’m not involved in it, please nobody tarnish me with the same brush.
"I think it’s ridiculous and that’s all I’ve got to say on it."
The Sun newspaper reported that Price and Woods had been spotted holding hands at the airport and that they shared a weekend getaway in Spain together over Easter.
Meanwhile the Mail Online published pictures of Price taken at a horse stables on Tuesday after Easter weekend, without her engagement ring on.
Price has not commented.
Speculation that the couple have split began last month when Woods deleted all images of Price from his Instagram account and the model and mother-of-five stopped wearing her engagement ring in public.
Price began dating Woods in June 2020 and in April 2021 they announced they were engaged to be married – her seventh engagement.
Woods recently spoke out after he was charged with a public order offence in relation to an incident last year.
He said the charge related to him arguing in the street and using foul language, but suggested it was wrongly being linked to reports last year that a man had been arrested on suspicion of assaulting Price.
Price was involved in a drink-drive crash in September last year and escaped a jail sentence shortly before Christmas after pleading guilty to the driving offences.
The former glamour model, who has previously spoken about her treatment for cocaine addiction, returned to The Priory rehabilitation clinic following her arrest in September.
The former glamour model — who was declared bankrupt in 2019 — is mother to 19-year-old son Harvey, whose father is footballer Dwight Yorke; she shares Junior, 16, and Princess, 14, with first husband Peter Andre; and Jett, eight, and Bunny, seven, with third husband Kieran Hayler.
Watch: Carl Woods pled not guilty to the public order offence