The EastEnders actress called off her wedding last month after discovering that Morse had sent lewd emails to an old girlfriend.
Morse has since accepted that Wallace "did the right thing" by cancelling their nuptials and this week publicly apologised for his actions on This Morning.
Speaking to The Sun, Morse claimed that he had managed to win Wallace over with his on-air plea and the pair would be meeting once the 39-year-old is able to take a break from EastEnders filming.
"I made a complete muppet of myself talking to her on TV but it's worked," the catering boss said. "Well, not 100%, but she's talking to me now a little bit.
"[We will meet] maybe next week. I don't want to say too much in case it jeopardises things. She says she'll consider meeting me soon. I don't want to mess up again and lose the best thing that's ever happened to me."
> Jessie Wallace 'hides' on EastEnders set to avoid ex-fiancé Vince Morse Get the Inside Soap magazine on your iPhone or iPad