Kiernan, is among a list of targets that have been drawn up by the Ibrox hierarchy as they look to secure promotion at the second time of asking. The defender, 24, played on loan at Brentford during Warburton’s time at the London club.
Warburton says that he is making headway on a number of potential new signings, including 35-year-old John Eustace who is available as a free agent after being released by Derby County.
Warburton told Sky Sports News HQ: “We’re making progress, there’s a number of targets. As you can imagine we have to be discreet and work to get the deals done but we are hoping for a positive few days ahead.
“It’s about making sure that any deal is right for all parties and that’s the main aim of all our meetings at this moment in time.
“I’d like to bring Rob here he is a very talented player but as I say we are not at the end of the good negotiations. I know him very well from earlier in his career, technically gifted, six foot three inches. He was comfortable at Championship level down south and if we can get him, he would be a good addition.
“It’s about looking at the squad and getting a young, hungry squad that want to come here and play. At the same time you need one or two senior mentors to look after them – both on and off the pitch. It’s about getting the balance right – making sure they are good enough to go out and play in front of 45,000 and it’s also about what they bring to the club off the pitch.
“It’s about us doing our homework, getting the balance right, and people like John Eustace are few and far between. We have just had a chat about him no more than that. I have been given a number of names and hopefully over the coming days we will have some news for you.
“Scott Allan of Hibs is another one I’ve been alerted to but he is just one of 100 players given to us and right now it’s about us doing our homework and we have to create an environment here where talented players want to come and play for Rangers.
“The training ground, stadium, we have to make the right environment and if we can do that we will attract the right players. But right now there’s meetings taking place and hopefully we can make some good progress.
“We’d like to get some deals done this week but the situation is the first competitive game is the 25th of July so we have to be aware of that… but we can’t rush into anything as the biggest mistake we could make is to panic and get the wrong players in at the wrong time.
“We have to get players who will add value here. I keep saying it, time and time again, so I would rather not rush into it but make sure we get the right people.”