The McLaren driver told Sky Sports television on Thursday that the approach came after Australian Daniel Ricciardo stunned Red Bull by deciding to join Renault in 2019 rather than accept a new deal.
"From one of the top three teams, I already had an offer a couple of times this year," Alonso said.
Asked whether that was Red Bull and Ricciardo's seat, he replied: "Yes."
The Spaniard's comments appeared to be at odds with Red Bull boss Christian Horner, who suggested after Ricciardo's decision that Alonso was not under consideration.
"I have huge respect for Fernando, he is a great driver, a fantastic driver, but...he's tended to cause a bit of chaos wherever he's gone," Horner had told the official Formula One podcast.
"I'm not sure it would be the healthiest thing for the team for Fernando to join. Our preference is to continue to invest in youth than take a driver who is obviously close to the end of his career."
McLaren announced Alonso's decision on Aug. 14, coincidentally the Spaniard's racing number.
The 37-year-old, who won his world championships with Renault in 2005 and 2006, was out of contract at the end of the season but McLaren had been keen for him to stay.
Red Bull are switching to McLaren's former partners Honda next year and Alonso had been strongly critical of the Japanese power units during their time together.
Speaking separately to reporters, Alonso again hinted that his retirement might not be definitive.
"Right now I am thinking that it's a goodbye, but life changes very quickly," he said.
"Life also taught me in the past how things may change. In a couple of months' or years' time. So...it's to leave the door open. I don't have the crystal ball to know what is going to happen in the future."
(Reporting by Alan Baldwin, editing by Ed Osmond)
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