The Republic of Ireland international was reportedly in South Yorkshire on Tuesday to undergo his medical ahead of a season-long loan switch.
Clark, left out of the Magpies’ 25-man Premier League squad for the second half of last season, had been training with the under-23s after returning for pre-season.
The 32-year-old had previously been an important player for United as he most notably helped the club achieve immediate promotion back to the Premier League in 2015/16.
Clark, who signed from Aston Villa ahead of that promotion campaign, has made 128 appearances for Newcastle.
His time on Tyneside is set to come to an end however, with the defender out-of-contract when his proposed loan move to Bramall Lane expires.
Blades boss Paul Heckingbottom yesterday (Tuesday) confirmed a deal for Clark was in place.
What Paul Heckingbottom said
“We are looking to do something on loan,” Heckingbottom revealed. “It’s not definite, but hopefully it will be pretty soon. I am expecting it.
“If we get it done, it will be for his experience and he has got promotions out of this league.
“He’s good in both boxes and gives us that balance on the left-hand side with Robbo (Jack Robinson) and he ticks a lot of boxes for us.”
Should a move go through as expected, Clark will be the third Newcastle player to join a Championship club this summer after Freddie Woodman (Preston) and Jeff Hendrick (Reading).
The Blades are aiming for promotion next term after losing to Nottingham Forest in the play-offs in May.