Striker Ferreyra was one of six players to return late to Ukraine last week, citing fears for his safety as the political tensions in the region continue.
The 23-year-old Argentine has since apologised for his tardiness, but could be set for a move away from the club if Pardew has his way.
"It's something that is not done, but we're working to see if that can happen," the manager told BBC Newcastle.
"Facundo is a good presence on the pitch, a big guy at 6ft 2ins, a player who has gone to the Ukraine and has been okay.
"If we manage to secure him, he would be a player who we'd expect to do a lot better here."
Ferreyra joined Shakhtar from Velez Sarsfield last season and scored six goals in 13 Ukrainian Premier League appearances.
Pardew said on Thursaday that the Premier League club were monitoring QPR striker Loic Remy's situation after his move to Liverpool fell through.
However, the Newcastle boss revealed on Friday that he does not expect the France international to return to St James' Park, where he enjoyed a successful loan spell last season.
"We've not really had much contact with Loic and I don't see that evolving if I'm honest," he said.
"Whatever happened at Liverpool is irrelevant really, because he's had plenty of chances to come to us.
"We've made it clear we'd want to have him but it hasn't really happened and therefore you sometimes have to say where is the line drawn? Maybe that one has gone away."