Hudson has been linked to Rodriguez for the last few weeks and has been spotted in the audience cheering him on during recent Yankees games.
Insiders claim the couple is taking steps towards making its romance public -- and Hudson has even introduced A-Rod to her 5-year-old son, Ryder.
A source tells People magazine, "It's somewhat serious. He introduced her to a bunch of his friends."
Rodriguez was previously alleged to be dating Madonna following her divorce from director Guy Ritchie, while Hudson, who shares Ryder with ex-husband Chris Robinson, recently split from on/off lover Owen Wilson.
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