The `Desperate Housewives` star - who is in the process of divorcing husband Tony Parker - has enjoyed a string of dates with singer Eduardo Cruz, the younger brother of Penelope Cruz.
A source told America`s OK! magazine: "He`s there at least three nights out of every four - he turns up and he leaves the next morning. They are trying desperately to stay beneath the radar."
The new couple reportedly met at a party and had been "flirting" for a while before 25-year-old Eduardo was spotted with Eva in her garage on Christmas Eve (24.12.10).
The actress` publicist stated: "Eva and Eduardo are friends."
Eva, 35, was married to Tony for three years before filing for divorce in November.
However, the pair are attempting to keep their divorce civil and were spotted having lunch together last month, with pals saying they met to "work out the details" of their split.
The heartbroken star has recently been comforted by close pal Victoria Beckham, who urged all their friends to rally round and support the actress through her marriage split.
A source said: "Victoria has rounded all the girl troops in their inner clique so they can have some girly time and relax. She has given her some sexy VB dresses to cheer her up and is planning a night out for Eva with all their celeb friends."