According to Bloomberg, people familiar with the matter noted Mr Jain - alongside a German-speaking board member - is likely to be the man chosen to succeed Josef Ackermann at the institution, which was formed in 1870.
The insiders noted Juergen Fitshen or Rainer Neske might be teamed with Mr Jain to allay concerns surrounding the appointment of a candidate who cannot speak the nation's language.
Daniel Hupfer, who manages assets at MM Warburg in Hamburg, said: "I'm a fan of an internal solution and Jain is a suitable candidate. I'd prefer dual leadership because his partner could cover the German political role that comes with the job."
Mr Jain became the favourite for the role following an announcement from UBS AG that Axel Weber had been hired as chairman.
By Tony Aynsley