Theresa May has stoked speculation that Nigel Farage could get a peerage for his role in the successful campaign for Britain to leave the EU.

The prime minister declined to rule out the idea as she was pressed by the Scottish National party at prime minister’s questions on Wednesday.

George Kerevan, an SNP MP, asked whether the government had had any official discussions about a peerage for the outgoing Ukip leader. May did not give an answer either way but smiled as she said: “All I can say to the honourable gentleman is such matters are normally never discussed in public.”

This week the prime minister’s official spokeswoman infuriated Farage by making clear Downing Street had no intention of involving him as a go-between in relations with the US president-elect, Donald Trump.

No 10 rejected outright the idea of a “third person” in the UK-US relationship, despite Farage being the first foreign politician to have a meeting with Trump since the Republican’s election victory.

However, giving Farage a peerage could be a way of recognising his role in taking the UK out of the EU. The Ukip leader was unsuccessful in running for parliament on seven occasions but played a key part in pushing David Cameron to hold an EU referendum and making the arguments for voters to opt for Brexit.

Asked whether Farage could get a peerage, May’s spokeswoman said on Wednesday: “There is a process.” She stressed that the honours system was used to reward those who “contribute to society and the community”.

Farage stood down as Ukip leader after the EU referendum, saying he had done his bit for politics. However, he returned temporarily after his elected successor, Diane James, refused to officially sign up for the post. The leadership contest is now being rerun, with Paul Nuttall, Farage’s former deputy, the frontrunner.

Farage has also been in the spotlight because of the US election, after he expressed support for Trump, spoke at one of his rallies and attended a series of television debates.

