Monye made way for the returning Chris Ashton in last Saturday's loss to Australia and has seen club colleague Mike Brown preferred on the left wing against South Africa.
The 54-12 victory over Fiji in England's autumn opener produced a try for Monye, but the match largely passed him by.
Premiership leaders Quins travel to Bath hoping to cement their place at the summit of the table, but Monye is looking ahead to New Zealand on Saturday week.
"I've got a big game coming up," said Monye. "If I can play well I'll be putting my hand up to play against New Zealand.
"You want to be constantly putting pressure on the guys that are in the team.
"The only way you can do that is by playing well for yourself. Whether that be for England or your club, you've always got to be performing.
"I spoke to (England coach) Stuart Lancaster. South Africa present a different challenge and Mike's got different strengths and weaknesses to myself.
"Mike has a fantastic left boot and he's been a unlucky not to play the last couple of games at full-back, so it's good he's been given a run."
Quins have resumed control of the Premiership following an early season wobble that saw them lose to Saracens and Exeter.
Successive narrow wins against London Irish and Gloucester have placed those defeats in the rear view mirror, but Monye insists they served a purpose.
"We needed a kick up the backside. Up until then we were winning games without actually playing very well," he said.
"In the league anyone can beat anyone and we went down to Exeter and they did that.
"Since then it's been great, we're top of the Premiership and top of our Heineken Cup pool, so things are going really well for us.
"We're exactly where we want to be at the moment and it's nice to know that since winning the Premiership we haven't let our standards slide.
"In fact we've kicked on and long may that continue.
"Bath have got a lot of players who are playing really well, but so have we.
"We don't fear anyone, and that's not arrogance, it's just pure confidence in what we're about."
Quins have been strengthened by the recovery of former All Black fly-half Nick Evans from an ankle injury, while lock George Robson and centre Jordan Turner-Hall have been released by England.
Bath captain Stuart Hooper returns to the starting line-up after being rested for last weekend's LV= Cup action with Kyle Eastmond restored to the right wing.
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