Their injury woes have increased in the meantime, with Scott McDonald, Stephen McManus, Danny Fox and Ki Sung-Yeung joining Scott Brown and Shaun Maloney on the sidelines.
They are also not in the best form, having won only one of their last five games in all competitions.
But Venus said: "We're ready for the game. We've got X amount of footballers at the football club, we want the game to be on.
"There are no excuses at all."
Venus, who was also Tony Mowbray's right-hand man at Hibernian between 2004 and 2006, admits Cappielow will be "a little bit foreign" for some of Celtic's players.
"I've not been to Morton since I was last in Scotland," he said.
"It's an old-fashioned stadium, it should have an old-fashioned cup atmosphere, which should be good.
"Players should enjoy playing the games. I used to enjoy it and I hope they do."
Midfielder Marc Crosas also expects unfamiliar opposition to be a problem for Mowbray's men, but he added: "Every game is difficult, even if you know the players or you know how they play."
The Spaniard believes the format of the Scottish Cup gives lower-league sides a better chance of an upset than its sister competition in his homeland.
He said of the two-legged Copa del Rey: "It's a bit different because you play two games every tie.
"The small teams don't have the same chances they can have in a tie like that here in Scotland."
Meanwhile, Neil MacFarlane will urge his Morton team-mates to set their sights higher than knocking Celtic out of the tournament.
The Ton midfielder, 32, went all the way to the final with fellow First Division side Queen of the South in 2008 only to lose to Rangers at Hampden.
And the former Hearts and Gretna player believes this clash could be a stepping stone to another thrilling cup run.
MacFarlane said: "We've got to believe that we can go on a run to the final.
"We've knocked out Dumbarton and we have been given a plum tie at home against Celtic and if we win then who knows what could happen, we could go on a run.
"We have to look after this game against Celtic first and it's going to be a huge game but we have to believe in ourselves that we can do it."
Celtic 1/6, Draw 6/1, Morton 14/1