Cardiff host Palace on Saturday in a Barclays Premier League relegation battle, and Solskjaer has questioned the timing of this week's reports regarding Zaha, who moved to Wales from Manchester United in January.
"We have had Wilfried coming on (against West Brom last Saturday), making an impact and - surprise, surprise - Palace want to sign him this week," Solskjaer said.
"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."
Whether he starts or appears off the bench, Zaha will be a key part of Cardiff's attacking armoury this weekend when they continue their fight for top-flight survival.
Cardiff are currently three points adrift of 17th place and safety with just six games left.
Defeat against Palace, currently 16th, would effectively leave them with one foot in the Championship, although they are fresh from salvaging a point at West Brom six days ago through an injury-time equaliser.
"We see it as an opportunity for us to claw our way back in on Palace," Solskjaer added.
"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."
Cardiff have scored three goals in each of their last two home games - beating Fulham before losing against title-chasing Liverpool - but Solskjaer knows Saturday's clash is likely to be a cagey affair, especially given the high stakes.
"If we score three against Palace I will be very surprised," he said. "They defend with their lives and put their bodies on the line.
"Palace won't give us any easy ride anywhere on the pitch. We've analysed them and looked at them, and tactically how we are going to approach the game.
"The fans might have to be patient. They might have to wait until the 95th minute again. It is going to probably be a stop-start game. We will have to try to break them down.
"We are scoring goals at the right time. We have goals in us, and we have the quality players in the last third to do that. In the last four games we have scored 10.
"We look like when we go forward we are going to score, but we must keep it tighter at the back.
"You have seen the change in them (players). Not since the Hull game (Cardiff lost 4-0 at home), but there has been a definite change in their mentality, attitude and the togetherness. They are ready for it."
Solskjaer, meanwhile, confirmed that Craig Noone is fit for selection this weekend after missing the last three games because of a groin injury.