According to sources close to Ms Alexander, a 42-year-old relationship therapist, the pair want to “move into a bigger place” together.
The 64-year-old Northern Irish GB News presenter and Ms Alexander are currently enjoying a luxury holiday to the Mediterranean, being snapped earlier this week arriving in Barcelona.
Holmes was seen driving a mobility scooter through the terminal while Katie pushed their luggage and a walking frame and they were also seen laughing and joking with other cruise passengers at Barcelona Port.
Speaking to The Sun, the source said: “Katie’s assured him she’s in it for the long haul and they’re both settling down nicely.
“They’ve been spending so much time at his Kingston flat that they’re even looking to move in together permanently.
“Eamonn doesn’t want to stay in his rented place as it’s too small, too expensive and, without air conditioning, gets very hot.
“It’s on the basement floor as well, with people looking in as they walk past all the time so isn’t private enough for them.
“With that in mind, they’re really keen to move into a bigger place in the country with lots of land.
“Katie will obviously be there to care for Eamonn as he grows older and thinks it’s best to do that somewhere without prying eyes.”
Holmes and Langsford, who were axed from This Morning in 2020, announced in May that they had broken up after 14 years of marriage, with a spokesperson revealing “they are in the process of divorcing”.
The TV pair, both 64, wed in 2010 after 13 years together and are said to be “determined to stay friends and keep things amicable”.
However, recent months have seen a raft of reports saying GB News presenter Holmes has become close with Ms Alexander.
According to the Daily Mail, Ms Alexander offers in-person, telephone and online therapy services, at a price of £45 for a 50-minute session.
According to the newspaper she is divorced and a mother to three children.
It was rumoured that the Northern Irishman had already popped the question after Ms Alexander was spotted wearing a sparkling diamond ring. But Holmes reportedly sent his estranged wife a message to reassure her that he was not engaged.
Two weeks ago Holmes spent his holiday from GB News showing Ms Alexander around Northern Ireland, with the pair spotted in Carrickfergus at American diner Papa Browns.
Last week Loose Women star Langsford directly addressed fans asking why she was still wearing her wedding ring despite her split with Holmes.
She shared a video on Instagram that saw her describing a recipe for a green smoothie she drinks each day. The TV host could be seen wearing her wedding ring in the clip, with one person asking in the comments section: “Why has she still got her wedding rings on?”
Langsford bluntly replied: “Because I’m still married.”