Solskjaer hopes to add at least another couple of players to his Cardiff squad this month, but is keen to stress he is not trying to follow a Manchester United template.
The 40-year-old has already been active in the January transfer window, bringing in midfielders Magnus Wolff Eikrem and Mats Moller Daehli from Heerenveen and former club Molde respectively.
The Bluebirds have also approached Hannover over the acquisition of striker Mame Biram Diouf.
Solskjaer has been reticent when it comes to putting names to his transfer targets, but admits he hopes there will be more new arrivals.
"I can't say anything on them (Zaha and Fabio) because they are players from Manchester United and I can't comment on players from other teams," said Solskjaer. "I am looking at strengthening my squad, but I can't say names.
"It is not about the number. I will work with the players I have here but if the right one comes up then I will do business like I have with Magnus and Mats."
But Solskjaer is adamant he is not simply looking to create an alternative Manchester United squad in south Wales.
"No, I'm creating a new Cardiff," he said.
"We need our own identity, it's not about emulating or copying anyone else, we want to play football.
"I want to develop Cardiff into a team everyone can be proud of of the way they play football. That we can dominate games like we have done at home this season a few times.
"It's not about copying anyone else, but obviously I want players I can trust and can play the way I want to."