Pitt, a former partner at Fried Frank Harris Shriver & Jacobson, stepped down last week from the chairmanship he had held for just 15 months, following a storm of criticism.
Most of his detractors had pointed to claims that there were conflicts in his role, since he had acted for a number of accountancy firms during his days as a lawyer.
However, more recently, his appointment of William Webster as chairman of the Public Company Accounting Oversight Board caused a welter of ill-feeling.
Webster had admitted that he was involved with internet group US Technologies, which had suffered from problems with its accounting controls.
Commenting on potentially welcoming back his former colleague, Peter Cobb, co-managing partner at Fried Frank, said: “It's too premature to even think about that. We have great respect for [Pitt], but it's not something I'd want to comment on.”
During his brief spell in office, Pitt, who had been handpicked for the role of SEC chairman by current US President George Bush, had vehemently denied claims that he would return to private practice, with the intention of assuaging fears that such a move would cause him to be soft on future clients.
Pitt, who had been a lawyer with Fried Frank since 1978, was one of the firm's most highly-paid partners. This qualified him as an 'immortal' – a group of partners who are remunerated outside the firm's lockstep.
But on taking the role at the SEC, Pitt took a cut in salary to just $133,700 (£850,000)a year.
A spokesman at the SEC declined to comment, pointing to Pitt's resignation letter to the US President as the only information the SEC chairman had released concerning his future.