The rumours surfaced after Lampard was tapped as a possible replacement for David Beckham at Los Angeles Galaxy, according to Now.
The Northern Irish presenter was axed from ITV's morning show Daybreak along with Adrian Chiles last week.
Bleakley will now replace Holly Willoughby as co-host of Dancing on Ice next year.
The presenter told Digital Spy that she and Lampard have yet to set a wedding date.
She said: "The honest truth is not yet. We can't quite plan anything - it all depends on the summer and whether Frank is picked for Euros or not.
"You assume possibly yes if you're lucky enough, but it doesn't mean that he is. If that's the case that he is, the whole summer is eaten up!"
> Christine Bleakley on Dancing on Ice: 'I've got big shoes to fill'