The rumour mill is on overdrive today following American reports Sir Paul McCartney is gearing up to propose to girlfriend Nancy Shevell.

The heiress is close to finalising her divorce from estranged husband Bruce Blakeman, and there are whispers the Beatles star is planning to ask her to marry him after that.

Getting serious: Sir Paul McCartney and Nancy Shevell on a romantic night out in  the Hamptons earlier this month

Chicago Sun-Times newspaper columnist Bill Zwecker reports: 'It looks like the romance between Paul McCartney and wealthy New York socialite Nancy Shevell may be on the verge of moving up a notch.  A source very close to the Beatles legend tells me Shevell may finally have worked out details of her divorce.

'When that happens, Sir Paul is expected to announce his engagement to his lady love - who would become his third wife.'

It follows reports that McCartney, 66, has been househunting in the same Manhattan neighbourhood as 47-year-old Shevell.

All you need is love: The pair have been dating since November

The pair have grown increasingly close since they began dating last November.

They enjoyed a romantic trip to Antigua in April and a road trip across seven US states last month.

And last week they were pictured having an intimate Japanese meal in the Hamptons on New York's Long Island.

Shevell, whose family has a multi-million dollar transport firm, is still to officially finalise her divorce from her politician husband of 23 years, Bruce Blakeman.

He is now reportedly in the running to become the next New York mayor.

Meanwhile, McCartney's former wife Heather Mills has reportedly been dropped from Donald Trump's reality TV show Celebrity Apprentice after she made 'ludicrous' contract demands.

Network NBC had her lined up to appear on the show but rejected Mills after she allegedly insisted on a clause in her contract to guarantee her a place in the final.

A representative for McCartney did not return calls.