The reality TV star has been seeing the Manchester United and England midfielder for several weeks after they were introduced via a mutual friend, reports The Sun.
The pair were said to have been spotted flirting during a dinner date in her hometown of Chigwell, Essex earlier this week.
"Tom's had an injury-hit year but Georgina has lifted his spirits. He's smitten and she's equally keen on him," a source said.
"His United teammates have ribbed him for dating a TOWIE star, shouting the show's catchphrases like 'shut up' at him.
"But they all know she's one of the best-looking girls on the show and appreciate he's done well for himself."
Dorset stated earlier this year that she does not want to date any of her TOWIE co-stars.
She joined the ITV2 show in series four, and has allegedly been told to "raise her game" if she wants to stay in the cast.