The Premier League club have reportedly been trying to capture the Lille full-back for the majority of the summer transfer window, as manager Alan Pardew looks to add to his defence.
And after a successful start to life at Newcastle, Cabaye is hopeful that Newcastle owner Mike Ashley can finally wrap up a deal for his fellow countryman, who he says wants to join the club.
"Mathieu has made a very difficult to decision to leave Lille but he has made the decision," Cabaye told The Journal.
"Now I hope Newcastle push for Mathieu and I want them to do the deal.
"I spoke with him two days ago and he told me he wants to come. I hope Derek [Llambias] and Mike Ashley will do the business now.
"He wants to play for Newcastle and I hope that he comes to Newcastle because, of course, he is my friend but also a very good player for Newcastle."
Newcastle ran out 2-1 winners over Braga at the weekend in preparation for the new season, when they will seek to repeat an impressive fifth-placed finish.
And Cabaye says he is happy with the pre-season performances, ahead of what he thinks will be an exciting year.
"It is very nice to be back with Newcastle. I have had four weeks of holidays but now I am glad to be back," he added.
"I am delighted to be back to build my fitness for the start of the Premier League season because it is going to be an exciting season for us.
"It was tough against Braga for the first five minutes because it is a long time to be away but after that it felt good and I felt like I was ready.
"I am looking forward to the next few weeks now."