West Ham boss Sam Allardyce is keen to sign the Chelsea forward on a season-long loan, but the Stamford Bridge hierarchy want a permanent deal for the Senegalese international.
The former-Hammer initially moved to Newcastle before making the switch to Chelsea in the January transfer window.
But a change of management at Stamford Bridge has pushed Ba further down the pecking order, with Jose Mourinho favouring Fernando Torres and Romelu Lukaku.
And the new Blues boss is reportedly trying to bring in another forward - Anzhi forward Samuel Eto'o is thought to be a target - which could pave the way for Ba's exit sooner rather than later.
The 28-year-old forward was an unused substitute during Chelsea's 2-0 win over Hull City on Sunday.
And Roma - who this week sold Daniel Osvaldo to Southampton for around £13m - are on the lookout for a new striker. They believe Ba could be the man to replace Osvaldo's goals and the Rome-based side are willing to buy the striker permanently.
West Ham, in contrast, prefer a season-long loan deal. The Upton Park outfit have just one striker available at present, with Andy Carroll currently sidelined.