According to reports, the couple were introduced by mutual friends and have been enjoying a long-distance relationship for several weeks.
Ryan, who plays Jason Grimshaw in Corrie, apparently went to see Justin Timberlake in concert with Amy a fortnight ago, however she has now flown to Mumbai.
The actress is from the Isle Of Man but moved to India in 2010 after carving out a successful career within the Bollywood film industry.
On 24 March, Amy shared a picture of herself on a night out with friends and Ryan is posing with his arm around her waist. Commenting on the snap, she said: "Fabulous night, with fabulous people."
A source tells Reveal: "Ryan and Amy have started seeing each other, they first met a few years ago and recently met up again.
"It's early days but they're great together - Amy is a successful Bollywood actress, with a schedule to match - so it's not easy for them to find time together, but they both really want to make it work."
Last week, before jetting off to Mumbai, Amy reportedly met up with Ryan in London. At the time, she tweeted: "Love waking up in the city... Haven't been this happy in a while #London "
Amy, 23, was crowned Miss Teen World in 2009. Reveal contacted Ryan and Amy's reps but they declined to comment.