The company said in a statement on Friday that Mr Street, the department store's managing director, has indicated to the group's chairman that he is "interested in running for the office, but at this stage has not been formally selected".
Mr Street will face formal selection process run by the Conservative Party.
"Should Andy be successful in his application, he has agreed with the chairman that he should step down from his role and a further announcement will be made to confirm the succession plan for the future leadership of the John Lewis brand," the firm added.
The news comes after months of speculation over Mr Street's political debut, and the potential end to his near nine-year tenure as the retailer's boss.
A Conservative spokesman said: "Our candidate will be announced shortly before the start of our party conference. At our conference in Birmingham they will set out their plans to make the West Midlands an even more prosperous and successful part of the country.
He added that the Tory candidate will be selected at a meeting of party members on September 29 and deliver a speech at the party's conference on October 2.
As well as heading up John Lewis, Mr Street has served on a number government bodies, including the Prime Minister's Business Advisory Group.
He has also been chairman of the Greater Birmingham and Solihull Local Enterprise Partnership, which is tasked with driving regional economic growth.
Mr Street's potential candidacy means he could become the first elected mayor of the West Midlands in May 2017.
The mayor would oversee regional affairs including road networks, housing supply and bus services and lead the combined authority covering Birmingham, Coventry, Dudley, Walsall, Sandwell, Solihull and Wolverhampton.