Rihanna's rumoured new romance with Ashton Kutcher is said to be heating up.

The Barbadian songstress has reportedly invited the Hollywood actor to go to London to be with her this summer.

She is set to perform at a few concerts in June and July and wants the Two and a Half Men star to come along for support, according to Britain's The Sun newspaper.

Rihanna and Ashton, 34, have been seeing each other for eight weeks apparently and it is his first high profile romance since splitting with estranged wife Demi Moore late last year following rumours of his infidelity.

Meanwhile, the 24-year-old performer has also now introduced Ashton to her younger brother Rorrey in a bid to get his seal of approval.

"Rihanna and Rorrey, who releases music under the name GQ, are close," a source told the publication. "So him meeting Ashton is a big deal."

"Rihanna clearly thinks things between them are serious."

The Umbrella star was seen arriving at Ashton's $10 million Hollywood Hills home last week around midnight and leaving four hours later.