Mildenhall has not yet received a final offer from the New York agency and it is unclear exactly what role he would adopt; however, the position of chief marketing officer is understood to be under consideration.
The move would pave the way for the London agency's chief operating officer, Shepherd-Smith, formerly the joint managing director, to return to the managing director role.
Mildenhall, who in addition to his managerial responsibilities looks after the agency's News International, five and Ask Jeeves accounts, said: "I have been in conversations with the powers-that-be about a move to New York for a long time now. Recently, our conversations have accelerated. There is still no hard job offer on the table but we are close."
"Being the right part of the management team at TBWA\New York would, quite simply, be a long-standing dream come true for me," Mildenhall added.
This latest shift follows a period of regular management changes at the London agency. In October 2002, Mildenhall and Shepherd-Smith were promoted to joint managing director positions after Garry Lace, then TBWA's chief executive, resigned to take the top job at Grey Worldwide London.
In December, a restructure saw Mildenhall take the sole managing director position while Shepherd-Smith took the role of chief operating officer, with responsibility for improving the agency's creative product and deepening relationships with key clients such as Abbey and the recently departed 3.
Shepherd-Smith joined TBWA from Leo Burnett six years ago to run its Nissan business. In 1999, he was promoted to head of account management.
Mildenhall, 36, joined TBWA from HHCL/Red Cell in 2001 as one of the agency's five managing partners.
He began his career as a graduate trainee at McCann Erickson in 1990.
He moved to Bartle Bogle Hegarty in 1992 where he worked on Audi and Coca-Cola. This was followed by a three-year stint at Lowe Howard-Spink, before its merger with Ammirati Puris Lintas, heading the Vauxhall and worldwide Smirnoff accounts.
Andrew McGuinness, the TBWA chief executive, said: "Jonathan has been keen to work in New York for a while now. As a global network, we are keen to move our talent around as much as we can. The strength of the team in London allows us the flexibility to consider such a move."