The 27-year-old Spanish defender supposedly told the South Wales Evening Post that he had been denied a transfer to Fulham even though the Premier League side had made a substantial offer for his transfer on Monday.
"What I know from my agent is that Fulham made an offer and it was the offer the chairman was asking for," Rangel has been quoted as telling the Evening Post.
"But then when everything about the deal was sorted and everything was ready, the chairman did not answer his phone or he turned it off."
However, Swans chairman Jenkins has denied receiving any financial deal for Rangel.
"I'm disappointed to read so many inaccuracies in the quotes from Angel," Jenkins said.
"At no time did Fulham offer any financial deal for our player apart from a loan option with the 'possibility' of a permanent deal at the end of it," Jenkins added.
"I am certainly not prepared to let a regular and quality Championship player with 18 months left on his contract leave the club for virtually nothing.
"As with every footballer at this club, if they don't want to play for Swansea City then they can leave, because it is important we maintain the fantastic spirit and togetherness within the squad that has taken us up to fifth in the Championship.
"But they will not leave until the deal is right for this football club.
"We've worked too hard and come too far as a football club to give players away for nothing to Premier League or other Championship clubs."