Lage said towards the end of November that Jordao had six weeks to prove he was ready for the first team, having been on the sidelines for several months with a knee injury.
The 23-year-old came off the bench in the FA Cup win over Sheffield United last weekend, and him staying beyond the end of the month now looks more likely than a loan move – although it has not been ruled out completely.
"I am very happy with him," said Lage on Jordao.
"He is working in both positions as a midfielder and I am very happy with him.
"He needs to continue to work. We start the season with three midfielders, we need one, and he's in our squad and training well.
"If he doesn't have any chance (to go on loan) of course he will stay with us, but if something appeared (a loan approach) and we understand it is better for him to play at a different level, that kind of thing can happen.
"But at the moment, in my opinion, he stays with us because he is doing very well and I am very happy with him."
Lage added on Jordao and fellow midfielder Luke Cundle: "Jordao has been working hard since the first day after he returned and he can help the team as a central midfielder.
"I hope we can give Luke more time with us and the chance to give him minutes. The competition (FA Cup) allowed this because we had five subs.
"He is very clever. I don't want to put pressure on him, but he knows we believe a lot in him."
Lage, meanwhile, is 'very happy' with how Morgan Gibbs-White has been progressing while on loan at Sheffield United and says he is in no rush to recall the academy product.
"I am very happy with him. I spoke him a few days ago and told him I am very happy with him," said Lage.
"We took the best decision in the beginning of September, he is playing well.
"Paul (Heckingbottom) is a great manager and I've known him since he worked at Barnsley, so I know he's in good hands.
"Everyone needs to prove every day that they deserve a chance to play, and I am very happy with Morgan.
"We have time for that decision.
"We are happy with our wingers. We have plenty of guys who can play there.
"Every time we need to take the best decision and what is best for the club and the player.
"We recalled the left-back (Ryan Giles) and centre-back (Dion Sanderson) because we don't have too many players in that position, but up front we do.
"We have time to understand what is best for us and Morgan."