The Warriors moved to the PRO12 summit with an eight-try 54-10 victory over Zebre last weekend, while the Welsh region fell to third following defeat in Edinburgh.
Four points are all that separate the league's top four sides with eight games remaining, making the Scotstoun shootout a potentially pivotal one.
And Kellock, who made his 150th appearance for Glasgow in the Zebre success, hopes that new Scotland call-up Tim Swinson will be able to play a part in helping his side continue their stint as the league's pace-setters.
"We know it is going to be a physical and abrasive game against the Ospreys," the second row told the Daily Record.
"But now we are top of the PRO12 we want to stay there, and it is vital that we make the most of our home advantage.
"Tim is playing really well right now and took his try superbly at Zebre, so he'll go into the Scotland mix.
"We hope to get him back for Saturday and the Ospreys game, but that is Vern (Cotter)'s call."
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