After overcoming a series of injury problems over an 18-month period, Jones has returned to the United first-team setup in recent months, but has featured just once during that time.
That appearance came in the 1-0 defeat to Wolverhampton Wanderers at Old Trafford back at the beginning of January, in which Jones impressed during a poor United display.
However, with a lack of game time since then, Jones was said to be on the search for regular first-team football until the end of the season, and Bordeaux had opened talks with United in recent days.
That deal appears to be off the table now though, with the 29-year-old said to have rejected the opportunity to move to France, according to transfer expert Fabrizio Romano.
The Italian journalist tweeted on his personal Twitter account on Sunday evening: "After agreement reached between Manchester United and Bordeaux, Phil Jones has decided to turn down this opportunity.
"Loan deal seems to be collapsed, as things stand."
Should Jones fail to secure a move away from Old Trafford before the transfer deadline on Monday, he will be left to fight for his place in the side ahead of the expiration of his contract in June 2023. body check tags ::