The 49-year-old actress is said to have been "flirting" and seeing more of her friend - who previously confessed to a boyhood crush on the brunette beauty - and now pals are desperate for them to officially embark on a relationship.
A source told America's OK! magazine: "They have been talking more than ever and they flirt anytime they spend time together. She's been his dream girl for most of his life, so it would be a fairy-tale ending for Chris.
"Friends are pressing Sandra to just finally give in and take their relationship to the next level. It's just a matter of time."
Sandra - who has a four-year-old adopted son, Louis - and Chris, 32, showed their "connection" at Hollywood eatery Cecconi's earlier this month, leaving their mutual pal and fellow dinner guest Chelsea Handler feeling awkward.
An onlooker said: "Chelsea looked like the odd man out - Sandy and Chris were talking and joking with each other for much of the time.
"Chelsea kept chiming in and they would include her but there seemed to be a connection between Chris and Sandy."
Friends of the 'Blind Side' star now hope the 'Captain America' actor can restore Sandra's faith in men following her divorce from Jesse James in 2010 amid revelations he had cheated on her with several women.