The 66-year-old is also hoping to bring Aston Villa striker Darren Bent to St James' Park before the close of the transfer window as the Magpies attempt to boost their forward line
Remy missed QPR’s opening fixture of the Championship campaign on Saturday, a 3-2 win over Sheffield Wednesday at Loftus Road, and Kinnear revealed the club were in talks with the Frenchman.
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"I would think maybe Monday or Tuesday we will be a position to say yea or nay, but I am very happy about how that deal is going at the moment."
Kinnear also revealed the Magpies were hopeful of signing Aston Villa striker Darren Bent, who no longer features in Paul Lambert's plans, but conceded they face competition for his signature.
"We were with Darren's agent for two or three hours, we thrashed out a deal,” Kinnear continued.
"We are still in negotiations with Aston Villa so there is a really strong possibility there.
"Again I hear the latest is that somebody else has all of a sudden shown interest in the player so we have competition from various clubs around the country, but I am not letting go.
"These are players that me and Alan [Pardew] have spoken about. These are players that we've all agreed at the club are the type of player we want to bring to Newcastle."