Scotland international McGregor has been out since aggravating a shoulder injury a month ago, while Steve Harper suffered a torn bicep while deputising against Arsenal on October 18.
That has left Bruce with third-choice Eldin Jakupovic between the posts.
And after composed showings at Arsenal and Liverpool, the Swiss shot-stopper was partly at fault in last week's 1-0 defeat to Southampton at the KC Stadium - a mis-hit clearance falling kindly for Victor Wanyama to impressively crash home from distance.
Hull have also been without key defender Michael Dawson and joint-top scorer Nikica Jelavic since their trip to the Emirates Stadium and, though Bruce expects them all to return after the international break, he remains hopeful they could be fit this weekend.
He said: "I'm hoping Harper, I'm hoping McGregor, I'm hoping Jelavic, and I'm hoping Dawson.
"After the internationals we do hope we can have them back because you can't be without your big players, especially down the spine of your team. Your goalkeeper, your centre forward, your centre half - it's never easy to replace."
Despite Jakupovic's costly error last week, Bruce backed the 30-year-old's mentality after being thrown into his Premier League debut in tricky circumstances.
Bruce added: "He's been terrific the lad. It's not easy for him to come on at Arsenal, not easy for him to keep goal at Liverpool and when you're a goalkeeper it's a bit of an unforgiving place.
"How many goalkeepers have you seen mis-kick one and it goes out of play, it goes to your man, it goes somewhere it shouldn't go. It went straight to Wanyama's feet and to be fair to the kid he smashed it in brilliantly.
"A goalkeeper has to put up with that, you need your mates then to get you out of trouble a bit, unfortunately for us last week against a very good Southampton team we were unable to do that."
