The 33-year-old singer has been dating the 37-year-old audio technician since May, following her split from former fiancé Christian Carino in February, and the pair are now said to be "working closely" on the pop superstar's new tunes at her Hollywood Hills property, which was once owned by late satire artist Frank Zappa.
A source told The Sun newspaper's Bizarre column: “Gaga has been hard at work on her new music for most of August and it’s been really fun as the studio is in her own home now.
“Dan hasn’t fully moved in but he has been spending a lot of time there and is working closely with her team.”
Gaga has seemed "happier lately" after embarking on a new relationship with Dan - who worked on her Las Vegas residency shows.
A source said recently: "Although she has been very busy, lately she seems happier."
Although things are heating up between the pair, Gaga is planning to take things "slowly" with Dan, who has worked with the likes of Camila Cabello, Bruno Mars, Justin Timberlake, KISS, Lenny Kravitz and JAY-Z, because it's still early days.
Friends of Gaga say she has completely moved on from feeling down after her split with Christian.
A source said: "All the attention for the movie ['A Star Is Born'] and her split from Christian was a bit much. She escaped to Mexico with friends twice just to get out of Los Angeles. She seemed tired and a bit gloomy."
The new music will be the 'Million Reasons' hitmaker's first since the 'A Star Is Born' soundtrack, which featured the hit single 'Shallow’.
The 'Million Reasons' hitmaker's last studio album was 2016’s ‘Joanne’.