The actress, who plays Kylie Platt in the ITV1 soap, admits that there is no evidence in scripts that the pair will have a storyline together.
She told Digital Spy: "I think it's important as Kylie does have that family tie on the street and I don't think it should be forgotten.
"I imagine the writers will do something with that. I haven't read any scripts yet which say that, but we'll just to have to see.
"Kylie and Becky did have a connection when they were younger, but then things became difficult between them when Becky moved out. I think something does have to be tied up there, definitely."
Referring to her lauded scene with fellow Corrie cast member Helen Worth (Gail Platt), Lane said that it was refreshing to indulge in more sensitive plots.
The star added: "It was nice that people got to see a different side to my acting and to Kylie's personality. I was really chuffed when that script came out and I got the opportunity to perform that with Helen Worth.
"I'm really pleased as the reaction to that was just phenomenal and it's still happening now - people are still tweeting me about that scene!"
In the past month, Gail has maternally comforted Kylie through her battle to win back son Max.
> Digital Spy interviews Paula Lane (Coronation Street's Kylie Platt) on Becky, Gail and more
> Corrie's Paula Lane: 'Kylie getting Max back would be fabulous'