The 21-year-old is highly thought of at Dean Court but has made just three career appearances to this point.
The player agreed to a new two-and-a-half-year contract this past January.
It is understood that manager Eddie Howe is keen to send Simpson to Ibrox as he wishes to give him more first-team opportunities.
Gerrard is looking to provide some competition for places in his centre-back corps with Nikola Katic and Connor Goldson the only experienced options at the position.
Meanwhile, the Sunday Express reports that Rangers are weighing up a £2million offer for Croatian defender Borna Barisic.