"Good luck is all I say to Theresa May," Alexander Stubb, vice president of the European Investment Bank (EIB), told CNBC's Silvia Amaro on Tuesday, when asked what advice he had to offer to her. The EIB is the EU's official lending institution.
Stubb, who formerly served as Finland's prime minister, said May probably has the "toughest PM job in the world" because "she has to negotiate a package which she knows in the heart of her hearts is not a good deal for the United Kingdom or for Europe."
"And on top of that," he added, "she has her own barking at her ankles from morning to night, so my only advice is just hang in there, good luck and I feel for you."
Stubb was referring to lawmakers within May's party, who are displeased with her so-called Chequers deal. May's Chequers plan would see some alignment between the U.K. and the EU continuing after March 29, 2019 in terms of trade and regulations although the deal foresees the U.K. being able to stop the free movement of people from the EU. It also foresees the U.K. being able to strike independent trade deals elsewhere.
Some lawmakers in May's reining Conservative Party, including former Foreign Secretary Boris Johnson, have condemned the plan aggressively, arguing it strays from what the British public voted for in June 2016.
On the topic of the possibility of Westminster and Brussels reaching a Brexit deal, Stubb said: "Usually these things have a tendency to take a while, so I wouldn't bank on getting a deal this week."
A big sticking point in talks between the two parties is that of the so-called Irish backstop, a safety net aimed at preventing the imposition of a hard border.
May is heading to Brussels this Wednesday to address the European Council, a collective of all the EU member states' leaders. Tusk, formally inviting the PM to the meeting on Monday, said a "no-deal" situation — where Britain withdraws from the EU without a deal — "is more likely than ever before."
Stubb said that, once the U.K. and EU agree to a Brexit arrangement, there could still be hurdles ahead if it doesn't get domestic backing.
"I have always said from the beginning that I'm sure that the European side will find a compromise and a negotiation solution, but the only thing that at the end of the day can derail Brexit is probably a decision by the Conservative Party, a decision in parliament or a new referendum," he said.
"So the ball I would still say is in the court of the United Kingdom. They have to decide what they do."
Stubb is also a candidate to take on the top job at the EU. He is among those vying to replace Jean-Claude Juncker, president of the bloc's executive body, the European Commission, once Juncker's term ends next year. Juncker has said he will not seek a second term as the commission's chief.