Lindqvist, who is going through a divorce with her plastic surgeon husband Ritu Chopra, is currently not in a Relationship with the actor.
According to E! News, Wilson has known about the pregnancy for several months and is "very supportive" of her.
"They get together for dinner and see each other fairly often. Owen has shown a desire to be involved with ultrasounds and doctor appointments. He's definitely invested in their unborn child," a source said.
Lindsqvist has no plan on pursuing a relationship with Wilson after her divorce is finalized or after the baby is born.
The 44-year-old star is already a father to son Ford with former girlfriend Jade Duell.