The 26-year-old joined the Rossoneri from Marseille in the summer but has struggled for a regular first-team berth.
Taiwo had been linked with a January move to injury-plagued Arsenal but now looks set to join QPR, with completion of the deal subject to a work permit.
The west Londoners confirmed the Nigeria international is "very close" to signing on their official phone-in show, London Call-In.
Several media outlets have reported the signing as completed, but QPR said they are "waiting for everything to be put into place before we make an official announcement".
Reports suggest Taiwo will pen a six-month loan deal and he was pictured with manager Mark Hughes on Twitter on Thursday afternoon.