According to The Mirror, show bosses are considering pitting the Weatherfield veterans - played by Barbara Knox and Eileen Derbyshire - against each other in the coming months by having them compete for the attentions of a man.
It is thought that Dennis Tanner, who makes a surprise comeback in next week's episodes, could be the male in question.
A show source told the newspaper: "Barbara and Eileen are great actresses and will love a meaty storyline to get their teeth into. One idea is for Rita and Emily to fight for his affections."
Philip Lowrie's return as Dennis, one of Corrie's original characters, was announced back in January. He is expected to remain on the cobbles for six months.
Last year, Rita was seen clashing with Audrey Roberts (Sue Nicholls) after they both took a shine to charmer Lewis Archer, played by Nigel Havers.
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