Townsend will officially take over at Scotstoun in time for the start of the 2012-2013 RaboDirect PRO12 season but will step down as Scotland's assistant coach after this weekend's match against Italy in preparation to lead the Warriors.
Kellock is adamant the upheaval won't affect the Warriors' charge for a play-off spot in this campaign and wants the fans to help make the next two months a memorable end to Lineen's nine-year involvement with the club.
"I would ask them (the fans) to back us, to support us," Kellock told the Herald.
"They will have opinions. That's part and parcel of being a supporter, but ultimately I would ask them to support us.
"We will go out there and give our all and that goes not just for the players but everybody involved and that won't change and I would like to think that's why they support us.
"He (Lineen) spoke about this year and obviously touched on what was happening.
"He said there are seven games left and he looked at the position we've put ourselves in and what needs to be done.
"Any one of about six or seven teams could still qualify for the top spots and we know that.
"So we've got to continue winning and use the momentum we built up at the Ospreys.
"There's huge motivational factors for us to do well this year and this adds to it. Hearing Sean speaking with such passion in the meeting only adds to the desire we have for this to be our best ever season."
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