The pair, who play on-screen couple Maria Connor and Chris Gray, were spotted shopping together at Kendals department store in Manchester on Friday and their relationship is said to be an "open secret" on set.
A source told the News of the World: "They are in love and feel they will be together forever. If it lasts fair play to them.
"But they have only known each other for a short while. Now they are spending all their spare time together."
Thorp, who recently split from his wife, was previously reported to be comforting Smith after her own marriage to husband of five years Matthew broke down earlier this month.