Rangers have secured the signature of Wigan Athletic's Rob Kiernan, hours after Danny Wilson became Mark Warburton's first signing as manager.
The 23-year-old, who was Hearts' captain, signed a three-year deal.
He failed to become a regular at Anfield but shone at Hearts following a move to Tynecastle.
Warburton said on Monday the former Scotland Under-21 international was one of the players attracting his interest and he is to be presented to the media in Glasgow on Tuesday.
Veteran midfielder John Eustace is also a target for Rangers after being released by Derby County.
"We are making progress," Warburton said. "We hopefully have a positive few days ahead.
"There are a number of targets and, as you can imagine, we have to be discreet."
However, Warburton stressed that, while he was looking for a couple of experienced leaders, he was mainly targeting young, "hungry" players with potential and who "passionately" want to play for Rangers.
"I think marquee signings are dangerous," he said. "The biggest mistake we could make is to panic and get the wrong players at the wrong time.
"The club we have just come from, Brentford, the average age was 23 and a half I believe, and we had a 33-year-old and 34-year-old in that."
Eustace, who had a spell on loan to Dundee United from Coventry City before time with Middlesbrough, Stoke City, Hereford United and Watford, has been earmarked as a potential captain.
"People like John Eustace are few and far between," said Warburton of the 35-year-old. "People like John are ultra-professional on and off the pitch. They are great role models.
"They are playing the game at a very high level at 33, 34, 35 because they look after themselves, they train well, they eat well, they conduct themselves well.
"If you look at his record and the win ratio when John's playing, it's really important. He had a big role to play at Derby over the last few years."
Meanwhile, Warburton said Hibernian midfielder Scott Allan was only "one of a hundred" players Rangers were considering and expressed no knowledge of being linked with Aarhus central defender Jens Jonsson.