Price and the Argentinian model began dating last year while she was still legally married to her then-husband Alex Reid.
She later suggested that she may one day marry Penna but the couple split in the autumn.
Rumours that the couple have reunited were sparked by recent Twitter communication between them.
A supposedly "close friend" has now told Heat: "Jordan wasn't sure about getting back together with Leandro. But now things are starting to heat up again."
The pair have been photographed at London's Nobu restaurant and the Rose Club nightspot.
Penna this week posted a photo on Twitter of Price running in the Brighton marathon, adding a heart symbol alongside the link.
Last month, it was reported that Penna had proposed to Price "completely out of the blue" on Christmas Day.
Price's first husband Peter Andre recently claimed that the glamour model wanted to get back together with him, a suggestion she quickly denied.
> Katie Price: 'I don't have sex on the first date'
Watch Katie Price and Leandro Penna's greetings from Spain last summer below: