The Toffees were beaten 4-1 by Southampton on Sunday and look worse under caretaker boss David Unsworth as every game passes.
Pulis was fired by West Bromwich Albion last week after a poor run of results.
He has a reputation as an effective but limited boss, unable to propel the Toffees to compete for Champions League places liked they dreamed off at the start of the season.
Nonetheless, Kilbane feels Pulis would be a sensible appointment considering relegation is more likely than a top four finish.
He told BBC Sport: "They were supposed to be getting someone to take them to the next level, which was what Koeman was meant to do.
"But Everton have now slipped into such a bad position that Pulis is the sort of name that you think could fit the bill.
"He might not be a long-term appointment, or the man to take a team into the top six, but he is well known for keeping teams up and survival is what this season is all about for Everton now."
Everton are in 16th place at present, just two points above the relegation zone and have already crashed out of the Europa League.
Their season is going from bad to worse and Pulis could be the man to temporarily stop the bleeding, before they end up getting dragged further into the mire.