Anderson, 52 – who played Margaret Thatcher in Netflix show The Crown – and Morgan, 57, reportedly split “amicably” in December after four years together.
While neither Anderson nor Morgan have publicly commented on the split, it has been reported that the relationship “had run its course”.
Now reports have suggested that Morgan has moved on with film producer Khan, 46.
The Mail on Sunday reports that Morgan and Khan have been dating since the start of the year and “are already living together”.
According to a source, Anderson is said to be “bemused” at the new relationship, with friends saying that “she has certainly raised an eyebrow or two” at news of the romance.
Morgan – who is currently writing the fifth series of the Netflix drama – and Khan have allegedly been seeing each other since the New Year.
“They are old friends and are now in what they call a legit support bubble,” added the source.
Another source stated: “There was a bit of a process before Gillian and Peter split but nevertheless, this has all happened very quickly and has been quite a surprise.”
Khan was married to Pakistani prime minister Imran Khan between 1995 and 2004 and together they have two sons. She has also been romantically linked in the past to Hugh Grant, Russell Brand and Matthew Freud.
The allegations come after Anderson revealed that she and Morgan never lived together.
Speaking to The Sunday Times Style magazine last January, the actress explained it would be the “end” of their relationship if they cohabited.
“It works so well as it is, it feels so special when we do come together," she added.
The actress – who has three children from previous relationships – recently poked fun at being single, posting a photograph of her new dog on Instagram, along with the caption: "Meet my new gf Stella [sic]."
The Independent has contacted representatives of Anderson and Morgan for comment.
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