The pair recently completed work on Ek Deewana Tha, Jackson's first Hindi film, reports Mid Day.
"Amy has been spending a lot of time in Mumbai. She has already enrolled in an acting class and [is] brushing up on the language and diction," a source revealed.
"The young couple [are] always together. Even when she has to travel out of Mumbai, Prateik makes it a point to drop and pick her up from the airport. They recently even attended an awards event together," added the source.
The Liverpool model has already featured in a number of Tamil cinema projects, including Madrasapattinam.
Jackson will be seen next in Nikhil Advani's upcoming fifth Bollywood production.