Cardiff host Palace on Saturday in a Premier League fixture with both teams desperate for a win to boost their hopes of avoiding relegation.
This week, Zaha, who left Palace last summer to move to Manchester United before he then joined Cardiff in a temporary deal in January, was reported to be a target of his former club.
"We have had Wilfried coming on (against West Brom last Saturday), making an impact and - surprise, surprise - Palace want to sign him this week," said Solskjaer.
"I would like to sign him if we can. Wilf is a good player, but I don't think 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.
"Of course it (the situation) is (manufactured), but Wilf is fine.
"I have had words with him and he knows the game. I have not heard (Palace manager) Tony Pulis speaking about him. I am not sure if he is Tony's type of player."
Cardiff are currently three points adrift of 17th place and safety with just six games left in the season, while Palace are 16th and five points better off than the Welsh side.
"We see it (this weekend's game) as an opportunity for us to claw our way back in on Palace," added Solskjaer. "I don't go into a game worrying - there are enough worries in life - but, of course, it is an important game.
"We are running out of games. We have to go out there and give it a go and do what we can to get those three points.
"It's important to go into the game with the right temperament and the right excitement and anxiety levels. A cup final is a chance to win something, and this, for us, is a chance to get back into it.
"The end of the game last week I hope was a turning point. It was key. To be down like that and come back gave us a massive boost.
"This is the biggest (game) for me as Cardiff manager. I always prepare the same. This is the main game now. It's very exciting."