Sampdoria midfielder Vieira made his name at Leeds United, whilst Davies was a left-sided centre-back Chris Wilder targeted when Jack O'Connell suffered a season-ending injury in September. The Blades' failure to sign Davies increased tensions between Wilder and the board and he instead joined Liverpool in January, but is available again having failed to feature for the Merseysiders.
The Blades are yet to make a major transfer in or out this summer, Jokanovic's first as manager, but he hopes the first part of that equation will change, and that in-demand players Aaron Ramsdale and Sander Berge do not leave.
"There's people on the way," he said, whilst confirmed his interest in Vieira and Davies. "We're expecting in the next few hours there can be some news.
"Of course I hope it will be as soon as possible but you know how these things go.
"I am happy with the players I'm working with but like all the coaches around the world we need some support and some improvement.
"The club have shown me ambition to improve the squad and I am moving in the same direction as them.
"It's a strong experienced and good squad and I hope in the days ahead of us we'll make it stronger still with some fresh blood in the squad."
Ramsdale and Berge have been linked with Arsenal, but there is no desire from Jokanovic to move either on.
"I will be really surprised if these two guys don't start the game against Birmingham," he said. "In the 20-odd days ahead of us I hope these two guys will stay with us because they are important players in my squad.
"I know how this business is but I am thinking of them as part of my squad and that's it. There's the possibility they could exit of course but at the moment I'm not thinking about being without them.
Billy Sharp and Oli McBurnie returned to training this week and are in contention to face Birmingham on Saturday evening at Bramall Lane but Enda Stevens is not, having not yet been passed fit to join the group.
"He'll need a few weeks more," said Jokanovic of the left-sided defender. "I've not had the opportunity to work with him but I know him very well from the past and I hope he'll be a very important player for us."