The Scottish Premiership leaders have approached The Cherries over the prospect of bringing defender Jack Simpson and midfielder Nnamdi Ofoborh to Glasgow as boss Steven Gerrard looks to bolster his squad.
Gerrard is believed to be a long time admirer of Simpson, who is out of contract in the summer, but Rangers will have to move quickly with Cardiff City having already had a £750,000 bid accepted for the 24-year-old centre-back last week.
Commenting on the interest, Bournemouth boss Jason Tindall said: “I think that’s just credit to Jack and the performances he’s been delivering since he’s been in the team.
“All his hard work while he wasn’t in the team I think has paid off because when he came into the team he delivered some really good performances – hence why such a good and big club like Cardiff have come in for him and want to sign him.
“What happens beyond that is out of my control really. All I can say is I’ve been really happy with Simmo while he has been here.
“What happens moving forward is obviously not down to me."
Midfielder Ofoborh is also wanted elsewhere with Charlton Athletic boss Lee Bowyer confirming interest in the 21-year-old, while admitting the Nigeria U20 international has "a lot more attractive offers" from elsewhere.
Bowyer said: "I like the player but it's not going to be realistic bringing him here.
"There are a lot more attractive offers for him at a higher level and even some abroad as well.
"We're working hard to try and bring someone in and we're hopeful we can do that before the weekend."
Discussing the future of Ofoborh earlier this month, Bournemouth boss Tindall said: “If Nnamdi wants to stay at the football club, it is going to be down to him.
"He’s certainly a player we like and we want to keep."
Rangers are also in talks with Aberdeen over the possibility of signing Scott Wright during the current January transfer window, with the Ibrox outfit having already confirmed their intention to sign the highly-rated forward on a pre-contract this summer.