The 22-year-old has been the subject of Ibrox interest throughout January but the clubs have so far been been unable to reach an agreement on a fee for the former England youth international and Derby County youth product.
Whittaker had an impressive first half of the season on loan at Plymouth Argyle, netting nine goals and registering seven assists in 27 appearances to help the side reach the top of League One before being recalled by his parent club.
"He will be staying at Swansea I believe," admitted the Rangers manager during his pre-match press conference ahead of Wednesday's trip to face Hearts at Tynecastle.
Beale also insisted that Rangers are no closer to signing Nicolas Raskin from Standard Liege despite reports in Belgium claiming a £1.75million deal has been agreed with Standard Liege.
"No closer on deals at the moment, as soon as any updates in the next 24 hours we will make you are aware,” he added. “We are looking for a midfielder that strengthens the team and creates more competition. I want players here for the long term and to make us stronger right to now.
“Once the window shuts the coaching takes place and I am looking forward to that. We always have a different targets for every position – I am really pleased with the targets from our recruitment tam. We are all aligned across the club.”