Manager Walter Smith earlier confirmed club officials were in negotiation with both Stoke and Portsmouth, who have so far resisted the Glasgow club's attempts to sign front player Tommy Smith.
The Rangers boss is hopeful of signing at least one player before their Clydesdale Bank Premier League opener against Kilmarnock on Saturday and there could be more on the way.
Smith, whose last permanent signing was Maurice Edu in August 2008, has not given up hope of a deal being ironed out for Rapid Vienna striker Nikica Jelavic despite complications.
And he is determined to remain in the hunt for players right up to the end of the transfer window.
The deal for Beattie appears closest to a conclusion as Stoke look to recoup some of the record £8million transfer fee paid to Sunderland for Kenwyne Jones last night.
"We definitely need to bring in reasonably experienced players," Smith said as he helped launch a £3million Old Firm vehicle sponsorship deal with Lomond Audi.
"The three boys that we're talking to are good players and would enhance the squad, and that's the most important thing.
"Tommy Smith can play in wider areas of the pitch. We're still looking and will continue to look until the transfer deadline to bring in another one or two."
The 62-year-old added: "We've gone for a number of players that we haven't been able to get but we hope to rectify that in the next couple of days, and hopefully over the next fortnight will be able to bring in a couple more."
Talks over a £3million-plus move for Jelavic have been ongoing for weeks and reports claim the Croatia forward is at odds with his club over a pay-off.
But Smith said: "We are still progressing that one. The longer it goes on, the more doubtful it gets that it's going to happen.
"There has been a fair amount of complications that we didn't foresee.
"A lot of these things don't go smoothly and that one certainly hasn't, but we haven't given up hope on that one yet.
"These deals have been going on for a long time, three weeks or so, so it's a bit frustrating. We hope we can have a couple of them by Saturday."
Smith will continue to assess 20-year-old Arsenal winger Nacer Barazite, who played in a 2-1 defeat by Glentoran on Tuesday, and Honduras striker Georgie Welcome will remain at Murray Park after the weekend.
"He is still here," Smith said. "It's unfortunate we have not been able to get a game for him.
"We had a game in Northern Ireland but we have not been able to play him in any public game.
"We'll have a closed-door game next week and that will give him an opportunity to show what he can do.
"It's always difficult for anyone to show in a training session how he is going to go."
While Smith is keen to make at least one signing before the weekend, he is not perturbed at the prospect of relying on players who have won two consecutive titles for him.
Smith is days away from the second anniversary of his signing of Edu but he believes the transfer embargo previously imposed by the club's debt problems may have been a perverse benefit.
"If you look at our squad we probably have 14 relatively experienced players," he said.
"We don't have a big squad and we have to enlarge that. But I don't think there is any doubt that the fact we haven't signed a player for a couple of years has brought a good bond to the players we have.
"So it has been a benefit to us in terms of overall team spirit."