Kevin Thomson admits the idea Celtic and Rangers players don't look at the other's results is "a lie".
The former midfielder made over 100 appearances for the Ibrox club, winning two SPL titles before moving to Middlesbrough.
He's now involved in the Rangers youth setup, and he feels the senior team can press home their advantage as Celtic sit out matches due to Boli Bolingoli 's ill-advised trip to Spain.
Thomson said on Go Radio: "People that play for Rangers and Celtic and tell you they don't know what Rangers are doing, or don't know what Celtic are doing, it's just a lie.
"Of course you always look across the city to see what they're doing, what they're up to and how their results are.
"Then you need to take care of what you do.
"So if the team, the manager and the staff can get off to a good start and put points on the board it'll certainly put pressure on Celtic when they do play their fixtures that's for sure."
Steven Gerrard's side could have an 11 point lead by the time their city rivals return to action.
They take on Livingston on Saturday before welcoming Kilmarnock to Ibrox the next weekend.
Meanwhile Celtic have seen their weekend fixture against Aberdeen postponed and won't return to action until they face Dundee United on August 22.
