The shadow Brexit secretary, Keir Starmer, is in talks over a possible role with the law firm that represented Gina Miller in her court battle with the government over article 50, leading a Conservative MP to raise the question as to whether it could involve a conflict of interest.

Starmer, a barrister and director of public prosecutions before he entered parliament, is discussing the possibility of the paid advisory role with Mishcon de Reya, the firm said.

The Labour MP has previously given legal advice to the firm, according to his register of financial interests. He spent four months in 2016 as a legal adviser to the Mishcon de Reya Academy, an arm of the firm connected to learning and leadership.

Starmer was paid £4,500 a month for six hours of work, but gave up the role when he became shadow Brexit secretary in October last year. He is in talks to resume the same role, which would not be expected to involve direct interaction with clients.

After Starmer stepped down, Mishcon de Reya represented Miller, the investment banker who was the most prominent among a group of claimants who successfully argued that MPs and peers had to give consent to the triggering of article 50, which formally began the UK exit from the EU.

The government was forced to introduce emergency legislation after its appeal to the supreme court in January upheld the decision favouring Miller and her co-claimants.

Asked whether there was a worry that Starmer’s role could potentially involve any conflict of interest, his office referred the Guardian to a statement from Mishcon de Reya. It read: “We are in discussions with Keir Starmer about reappointing him as an adviser to the Mishcon Academy.

“His wide experience and previous association with the firm would enable him to play a key and unique role in shaping the work of the academy, which leads new thinking and develops the potential of everyone in the firm.”

Tory MP James Cleverly has written to Starmer asking him to explain the role, and whether it could involve any conflicts of interest.

“Mishcon de Reya have been an active participant in legal cases surrounding the United Kingdom’s exit from the European Union,” he wrote in a letter, released by the Conservative party.

“The firm stressed that the result of the referendum was not legally binding and supported anonymous claimants in their legal efforts last year.”

The letter cites a section of the MPs’ code of conduct, which says they should avoid conflict between personal and public interests, and states that Starmer’s role meant he “will be personally involved with drafting and speaking on legislative amendments on the EU withdrawal bill”.

Cleverly said that Starmer should explain his Mishcon de Reya role and how he will avoid any conflicts of interest, and explain whom he provided advice to.

Starmer was a leading human rights barrister before becoming the MP for Holborn and St Pancras in 2015. Called to the bar in 1987, three years later he was among the founders of Doughty Street Chambers, which specialises in rights issues. He served as director of public prosecutions from 2008 to 2013.

His register of interests shows that before taking the frontbench role, he received payment for one-off advisory work to other firms of lawyers.