Elon Musk has floated the idea of buying the budget airline Ryanair, escalating his public spat with the Irish carrier’s boss, Michael O’Leary.

The two outspoken businessmen have locked horns since last week, when O’Leary was asked whether he would follow Lufthansa and British Airways in installing Musk’s Starlink satellite internet technology on his fleet of 650 aircraft.

The Ryanair chief executive rejected the idea, saying that adding antennas to the jets would result in “2% fuel drag”, adding an extra $200m-$250m (£149-223bn) a year to its $5bn annual kerosene bill.

Musk said that interpretation was “misinformed” in a post on his X platform, prompting a tit-for-tat exchange of insults, with each calling the other an “idiot” and then the Tesla and SpaceX CEO saying O’Leary should be fired.

On Friday, the world’s richest person asked his followers on X whether he should buy Europe’s biggest airline, which is now valued at €30bn (£26bn), posting: “Should I buy Ryan Air and put someone whose actual name is Ryan in charge?”

He followed it up with a poll asking whether he should “Buy Ryan Air and restore Ryan as their rightful ruler”, with more that three-quarters of the nearly 900,000 respondents saying yes with three hours before the poll closed. Tony Ryan, the Irish billionaire businessman who co-founded the budget airline in 1984, died in 2007.

Ryanair’s X account joined in the mocking of Musk, posting in response to an X outage across the US last week: “Perhaps you need Wi-Fi @elonmusk?”

Musk wrote in a reply to a Ryanair post mocking him: “How much would it cost to buy you?”

It may look like idle talk, but the South African born billionaire has followed through on such threats before. In a social media exchange in 2017, he tweeted that he loved Twitter and when a journalist suggested he should buy it, Musk famously replied: “How much is it?” He bought the platform almost five years later in a $44bn deal and later renamed it as X.

However, airlines based in the EU must be majority-owned by EU nationals or citizens of Switzerland, Norway, Iceland or Liechtenstein under the bloc’s rules.

The row was prompted by an Irish interview on Friday in which O’Leary said he would take no notice of what the Tesla CEO had to say about installing wifi on Ryanair planes.

“I would pay no attention whatsoever to Elon Musk,” he told Newstalk. “He’s an idiot. Very wealthy, but he’s still an idiot

… What Elon Musk knows about flights and drag would be zero.”

He claimed adding a Starlink antenna to every jet would push the fuel bill up by “an extra dollar for every passenger we fly and the reality for us is we can’t afford those costs. Passengers won’t pay for free for internet usage; if it’s free, they’ll use it – but they won’t pay one euro each to use the internet.”

O’Leary, 64, also said he was “thankfully” too old to have any social media accounts.

Ryanair was contacted for comment.