The 28-year-old landed three perfectly-struck penalties from distance and two simple conversions in a faultless kicking display on Saturday.
Warren Gatland, Wasps' previous director of rugby, was always a firm believer that Van Gisbergen should go on and play for England.
And McGeechan is confident the player can make the step up to international rugby.
"I am sure he could. He is a quality player and he is very important for us," said McGeechan.
"I am sure that if you have players like that coming through, Andy Robinson needs the widest base possible to be picking from."
Wasps are notoriously slow starters and Saturday's victory was only their second opening-day win in seven seasons.
They were forced to come from 6-0 down after two Glen Jackson penalties but Van Gisbergen's boot and a brilliantly executed try from Tom Voyce earned Wasps the half-time lead.
Ben Skirving galloped over for Saracens immediately after the break but two more penalties from Van Gisbergen and then an injury-time try from Fraser Waters sealed the victory.
Waters' return to action was hailed by Wasps coach Shaun Edwards after the England centre missed virtually all of last season with an ankle injury.
"The maestro is back," said Edwards.
Saracens have taken great leaps forward under Steve Diamond - they staged a late season surge to qualify for the European Cup last year - but he rubbished predictions they are title contenders just yet.
"A lot of people think we will be in the top four but we have been in the doldrums for so long we need another year or two of consolidation before we can beat the likes of Wasps or Leicester," said Diamond.
"We kept them under pressure but we needed that little bit more composure. We didn't have the composure and we didn't show what we could do.'
Saracens lacked creativity behind their powerful scrum and will be looking to Andy Farrell to inject that vision - but he is set to be out with a toe injury for at least another week.
The limelight in part two of a double-header at Twickenham was stolen by old-timer Mike Catt, who upstaged Leeds' big-name debutant Justin Marshall as London Irish beat Leeds 27-11.
Catt had a hand in the Exiles' first three tries - finished by Rodd Penney, Delon Armitage and Justin Bishop - before Kieron Dawson sealed the bonus point with a late fourth.
London Irish director of rugby Brian Smith said: "Mike did a great job leading the squad and he created a lot of scoring opportunities. It was a real captain's knock."
Meanwhile, Leicester blasted out of the Premiership starting blocks with a crushing 32-0 victory over a woeful Northampton.
The Tigers, playing their first league game without retired England heroes Martin Johnson and Neil Back, sunk the Saints in emphatic fashion with tries from James Hamilton, Michael Holford, Alesana Tuilagi, Dan Hipkiss and Tom Varndell.
And it could have been a whole lot worse for Northampton had fly-half Andy Goode, the Premiership's top points scorer last year, not missed six kicks at goal.
The victory was built on a dominant display by their forwards, featuring impressive Premiership debuts from new signings Alex Moreno, Leo Cullen and Shane Jennings.
"I thought the forwards played very well. We thought we would have an advantage up front and we tried to utilise that. I thought lock James Hamilton fully deserved his man of the match award," said coach Pat Howard.
"But we have still got a lot to work on - I wouldn't get overly carried away."
Northampton flirted dangerously with relegation last season and on the basis of this display could face similar problems this time around.
Star fly-half Carlos Spencer tried his best to give Saints some momentum but had no platform to work on after Leicester's forwards took charge from the opening minutes.
Saints rugby director Budge Pountney conceded: "Leicester is a hard place to come to and at times we struggled to keep up."