Allardyce, now in charge of Premier League outfit Sunderland, was the manager of Bolton from 1999 to 2007.
O’Halloran, who joined Rangers from St Johnstone in the January transfer window, was in the youth rank at the Trotters during that time.
The 25-year-old, who is a versatile player and can play across the attack, has spoken highly of Allardyce and is disappointed to see Bolton struggling in the Championship at the moment.
“I joined Bolton at 16 after they had finished fifth in the English top flight,” O’Halloran told The Daily Record. “So it’s a shame to have seen their decline as a club.
“Jay Jay Okocha had just left Bolton when I arrived but Nicolas Anelka was there, as was El-Hadji Diouf and Ivan Campo. Sam Allardyce was very big on the analysis side.”
O’Halloran has also given an insight into training at Rangers.
“At Rangers we wear vests in training that measure how many high-intensity runs, how many sprints you are doing, so you can see how hard you are working during the week,” said the Scotsman.
“It helps the fitness coaches as well in terms of seeing how much distance you are running and how you adapt to sessions.
“After the games we also have our own little website. All our clips get uploaded onto that and we can watch our performance.”
Rangers are at the top of the Scottish Championship table at the moment with 72 points from 29 matches.
Mark Warburton’s side are 11 points clear of second-placed Falkirk and have a game in hand.
The Gers will return to action on Saturday afternoon when they take on Queen of the South at Ibrox in Glasgow in the Scottish Championship.