Simpson’s contract at the Vitality Stadium is set to end in the summer and he has been linked with leaving the Cherries in the ongoing transfer window.
Gers boss Steven Gerrard has been a long-term admirer of Simpson and is keen on taking him to Ibrox in the window.
Rangers are also eyeing roping in Simpson’s team-mate Ofoborh, who has less than six months remaining on his contract at Bournemouth.
And the Scottish giants made contact with the Dorset outfit on Thursday over potentially taking the Bournemouth duo north of the border.
Simpson was the subject of a £750,000 bid by Cardiff City last week, which Bournemouth accepted, but doubts have been cast over the switch since then.
24-year-old Simpson has started six Championship games for Bournemouth so far this season while Ofoborh’s involvement in the league ends with just three substitute appearances at present.
It remains to be seen whether Rangers make any concrete bids for the Cherries duo and succeed in luring them away to Scotland with two weeks left in the current window.