Whittaker spent the first half of the season on loan at Plymouth Argyle, scoring nine goals and registering seven assists in 25 appearances during an impressive spell with the League One leaders.
He has not played since being recalled to his parent club earlier this month having made only four Championship starts for Swansea since making a £700,000 move from Derby in February 2021. He has made 22 Swansea appearances in total - including nine under current boss Russell Martin - scoring five goals. He spent the second half of last season on loan at Lincoln City.
Rangers have been linked with a move for the former England youth international in the January window, with reports claiming that an offer has been submitted, and that Whittaker is keen to join up with Beale at Ibrox.
"He's a player that we know. I think he's a good player. There's no update on that yet," said the Rangers manager.
"To be fair, he's just come back off a loan and back at his parent club. They think he's done very well.
"He's Swansea's player, but he's certainly a player that I'm aware of from working down south. Knowing his background, I think he's a good player.
"We're looking at all areas, but obviously we're looking to bring in more goals.
"We've had injuries in the front line, we've not had Antonio [Colak] or Kemar [Roofe] fit. Rabbi Matondo has had an ongoing problem with his knee so he's not been available.
"Alfredo [Morelos] has a contract situation and so does Ryan Kent. So we have a gap in the forward areas to make sure that we're strong. We need goalscorers in the building."
Rangers are also believed to be closing in on the pre-contract signing of Norwich midfielder Todd Cantwell.
Beale added: "There's no update just now but I'm really pleased with how things are moving. No news isn't necessarily bad news.
"Everyone is on the same line and everyone is moving in the right direction.
"That's not specifically speaking about that player, that's just things in general.
"I don't want any short-term gaps. For me, it's about bringing in players who I think can make a big impact moving forward.
"There's ongoing discussions with players who are out of contract, so we're trying to look at what the squad is going to look like in 2023, 2024 and onwards.
"In the past we've made some key recruits that are still in the building now. It's important whatever decisions we make are the right ones.
"At the moment, with everything I'm hearing from behind the scenes I'm happy with."