The Argentinian was diagnosed in September, and is yet to feature this season.
Jonas was given the all-clear in November, with Pardew subsequently stating that the 31-year-old would return to training in December.
On Tuesday, the Newcastle boss declared that Jonas would return to the fold over the coming weeks, and would be given a fair chance to win back his spot in the side.
"Jonas is one of those people who livens up the training ground just by his personality," Pardew told reporters.
"Of course, with him recovering from his illness, that's been magnified.
"We are really pleased to have him back. He is finding his feet a little bit. He hasn't been around the ball much, but he looks in pretty good shape. We hope in two or three weeks, he will be in and around us.
"He is keen to get back in amongst us and earn his right to play in the first team again.
"Like any player, I have got to give him an even keel, and he will get that. Now it is up to Jonas.
"I know one thing: it will be emotional for him, and for us, when he does return. We are all looking forward to it."
Over the weekend, Hull City manager Steve Bruce declared that the whereabouts of on-loan Newcastle winger Hatem Ben Arfa were unknown, sparking rumours that the Frenchman's deal at the KC Stadium would be cancelled.
However, a return to St James' Park looks unlikely, with Pardew appearing to rule it out.
"He won't be coming back here, that's all I can say," he said.
