The Argentinian defender has been strongly linked with a move to the Etihad, but his Dutch parent club are reported to be insisting City pay the full £23 million asking fee.
Tagliafico is dating the gorgeous blonde model and social media star Caro Calvagni.
The 32-year-old, also from Argentina, has built up a solid following of almost 280k followers on Instagram, where she regularly shares snaps of herself on the beach, as well as other pictures of herself and Nicolas' glamorous life.
Posting on her Instagram this week, she shared a beautiful mirror selfie wearing a crop top and black jeans.
She also posted a cute video of the couple's dog spying on her taking a selfie from behind the bedroom door.
Tagliafico joked in the comments underneath the post: "I left him watching."
Caro and her left-back boyfriend have been dating for at least four years and went viral for a bizarre incident back in 2016.
Tagliafico was shown fouling his girlfriend while the couple had a playful kickabout on the beach in the Mexican resort of Cancun.
The powerful defender took Caro's legs out from under her as he went in for a crunching two-footed slide tackle.
But the model saw the funny side of it, sharing the video on social media with the caption: "Hahaha, he forgets he's playing with a woman."
Many people were quick to comment on the clip, with one viewer joking: "Hey Ref, foul!"
While another wrote: "No, she threw herself down on purpose."
Tagliafico has been strongly tipped to move to the Etihad, as Pep Guardiola looks to strengthen his defence for this season.
City have already spent more than £100m on defenders this summer after landing Nathan Ake from Bournemouth and Benfica's Ruben Dias.
Tagliafico has impressed for the Dutch side since signing from Independiente in Argentina two years ago and was a crucial part of Ajax's run to the Champions League semi-finals.
But the club are thought to be reluctant to lose a fourth senior player in the same summer, despite Tagliafico's desire to move to the Premier League.