Zaha, who is on loan at Cardiff from Manchester United, has been informed by Palace chairman Steve Parish that he would be welcome back at Selhurst Park, but Solskjaer has admitted that he is keen to keep the England international in Wales.
The 41-year-old told reporters: "We have had Wilfried coming on and making an impact and - surprise, surprise - Palace want to sign him this week. I would like to sign him if we can.
"Wilf is a good player, but I don't think that he is being drawn into this situation where it is suddenly brought up that his former club want to sign him just as he faced his old team. Palace is his past."
Cardiff host Palace on Saturday as they look for three points that would boost their survival hopes.