Press Association Sport understands the Magpies have made an undisclosed, but substantial offer for the 23-year-old Frenchman.
The move came on Wednesday morning, with Cabaye expected to complete his big-money move to Paris St Germain later the same day.
Grenier is one of a series of potential targets identified as the club drew up a contingency plan with speculation mounting that PSG would make a January move for Cabaye.
The France international has scored 12 goals in 89 appearances for Lyon.
However, his current manager Remi Garde has voiced his hope that the player will not be sold this month, and it remains to be seen whether or not the Magpies can tempt the Ligue 1 club to part with him.
Newcastle's valuation of Cabaye was in excess of £20million and although the fee they have agreed with PSG has not been disclosed, manager Alan Pardew has urged owner Mike Ashley and director of football Joe Kinnear to invest a significant proportion of the proceeds in a replacement.
Pardew was hopeful of making at least one January signing before the interest in his star man was formalised, and Borussia Monchengladbach striker Luuk de Jong was due to undergo a medical on Tyneside on Wednesday with a view to completing an initial loan move to St James' Park.
But a successful swoop for Grenier before Friday night's transfer deadline would provide a further boost to a club in desperate need of a new playmaker.
Pardew's men passed up a glorious opportunity to add another three points to their Premier League tally at Norwich on Tuesday night when they dominated, but ultimately came away with just a point from a 0-0 draw despite hitting the woodwork three times.
To make matters worse, they had leading scorer Loic Remy sent off late in the game, and he will now sit out Saturday's derby clash with Sunderland - a match his side cannot afford to lose - through suspension.
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