Kate Hudson’s rumoured fling with Madonna’s ex Alex Rodriguez has reportedly shifted up to the next level.

The couple first met earlier in the year but were only linked romantically last month after being spotted dining - and kissing - in New York.

Now Kate is said to have followed New York Yankees star Alex to Dallas, to watch him play in a three-game series against the Texas Rangers.

A source told People magazine: “It’s somewhat serious. He introduced her to a bunch of his friends.”

The source added that the couple - along with Kate’s five year old son Ryder from a previous relationship - stayed at the same hotel and were spotted working out together in the hotel’s gym. Afterwards, Ryder and his nanny went to watch Alex play at the field while she “stayed behind and watched the game from the hotel”: “She remarked several times about what a big baseball fan she is.”

Alex’s wife Cynthia filed for divorce a year ago after claiming he’d had a “spiritual affair” with the then-married Madonna. Kate separated husband Chris Robinson in the summer of 2006 and has since been linked to Owen Wilson, Dax Shepard and Lance Armstrong.