Ryan Heath, reporter for Politico’s Brussels Playbook, said European Union leaders feared the foreign secretary’s support base.
He added it was a “dirty secret” that they also did not want Jeremy Corbyn to win June’s General Election.
Speaking on the Today programme, on BBC Radio 4, host Justin Webb said: “What about the view of the potential leadership changes at the top of the Conservative party and indeed that would leave us with a new Prime Minister.
“Is there a kind of sense that Theresa May is as good as it gets for them, or what?”
Mr Heath replied that was “spot on” and EU chiefs “appreciated” the Prime Minister’s Florence speech last month, when she called for a two-year transition deal.
He said: “Spot on. It’s the dirty secret here in Brussels in that no-one here from the national governments that come here for leaders’ summits were really hoping that Jeremy Corbyn won the election in June.
“No-one is really hoping that Boris Johnson takes over from Theresa May because the view here is that Boris has the support of party activists.
“So if Theresa May were to destabilise herself or be pushed out, in a way where she wasn’t the Prime Minister anymore, Boris Johnson is the likely replacement and that scares people here.
“So they’re quite happy that Theresa May is there, they appreciated the spirit of her Florence speech.
“It’s not anyone’s desired situation but they would happily cope with it.”
Downing Street is “furious” about Philip Hammond’s “naive” handling of Brexit and recent comments that he was not going to spend money on a “no-deal”, BBC Newsnight revealed on Wednesday.
There is anger in number 10 at the “obtuse approach” of the Chancellor to leaving the EU, according to BBC political editor Nick Watt.
It stems from an article which Mr Hammond wrote in The Times which prompted the paper to run an analysis with a front-page headline saying, “Hammond refuses to budget for hard-Brexit”.
Speaking on Newsnight, Watt said: “There is immense irritation in number 10 over what is being described as the ‘obtuse’ approach of Mr Hammond to politics.
“There was not an actual problem with his article because that was approved – which he said he would spend the money but will only spend it when it is necessary.
“But there was an annoyance in Downing Street over how he handled his relations with The Times, which quite rightly and justifiably wrote a rather dramatic story on their front page.”