O’Halloran is on the books of St. Johnstone at the moment and has a contract until June 2017.
Scottish Championship outfit Rangers are interested in signing the 25-year-old forward in the January transfer window, with St. Johnstone manager Tommy Wright recently confirming of the Gers’ interest to The Daily Record.
Tavernier, who joined Rangers in the summer of 2015, believes that O’Halloran would be a good signing for the Glasgow giants.
However, the 24-year-old former Newcastle United right-back has stated that the Scottish forward would have to work hard to get into the team due to competition for places.
“I’ve only seen him when he played against us but he had a really good game that day,” Tavernier told The Scottish Sun about O’Halloran. “He showed a lot of pace and his finishing was good.
“If the deal gets done the main thing is that — like everyone who comes here — he is going to have to work hard to get into the team.
“No one here is assured of a place, but if he comes it will make for more competition for places and that can only make the team better.”
Ranges are at the top of the Scottish Championship table at the moment with with 50 points from 20 matches.
Mark Warburton’s side are two points clear of second-placed Hibernian and have a game in hand.