Show producer Phil Collinson last year expressed his desire to see the pair tie the knot, and a report in The Mirror today suggests that the ceremony could go ahead in the summer.
Rita, played by Barbara Knox, will apparently "seriously consider" getting engaged to Dennis later this year.
A Coronation Street source commented: "It is the talk of the cast that Rita finds herself falling in love with Dennis - and that she could actually become Mrs Tanner after all those years since Elsie was a fixture around the cobbles."
The insider added: "Who would give her away is the big question being asked at the moment - there is one name in the frame to walk her down the aisle or be with her at the registry office, and if that materialises there wouldn't be a dry eye up and down the country."
Coronation Street chief Collinson previously said that it would be "great" to see Rita and Dennis marry.
Speaking last November, he explained: "Rita genuinely loves Dennis very much. Their storyline harks back to 1964, when he looked after her and took her in. Now he's grown to love her because she's been able to look after him.
"I like that we can tell a love story of people in their 70s, and it's a relationship that we're really committed to. I'd love for Rita to have a wedding, so watch this space! And if we did have one, she'd be Mrs Tanner - how great is that?"
Philip Lowrie, who plays Dennis, returned to Coronation Street in early 2011 following a 43-year absence.
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Watch a preview of Friday night's Coronation Street double bill in the video below: