As it stands, Armstrong - who has scored once in 14 Championship appearances this season - is due to return to St James' Park in January, but Madine is keen for his teammate to remain at the Macron Stadium until May.
The 27-year-old told the Bolton News: "Adam is a brilliant player. He is a great finisher and maybe not everyone has seen that yet. But we do see it every day in training.
"He hadn't scored for a few games but he's got off the mark now in the league so I think he'll push on from there. He doesn't let it get him down. His finishing is amazing in training and up there with the best I have seen.
"I know the gaffer will probably want him to and I know Adam will want to stay as well. Because we have a good bond as a team. I hope he stays. I am sure he will."
Before the international break, Armstrong scored the decisive goal as Bolton registered a 2-1 win over Norwich City.
However, despite the club extending their unbeaten record to five games, the Trotters remain in the relegation zone.