Gatland confirmed he held talks with the 22-year-old New Zealander over a potential move to Wales.
And Cardiff Blues are understood to be keen on offering a contract to the fly-half, who also plays full-back, given they are losing goal-kicker Leigh Halfpenny to Toulon this summer.
Anscombe, whose father Marc is coach of Ulster and mother Tracey was born in Wales, is weighing up his options given he will soon complete his one-year contract at Waikato Chiefs.
But Gatland has warned Anscombe the clock is ticking for him to force his way into the reckoning for next year’s World Cup.
Gatland said: “I have spoken to him and his father and we would relish the opportunity for him to come to Wales and potentially be involved in 12 months’ time. But I was honest and said, in terms of the squad harmony, if he was going to come then we would prefer him to come now so he will have a year of playing in Wales.
“You can’t parachute someone in for the World Cup. Bringing in someone from the cold would not be good for the squad. He understands that so the ball is in his court.”
Anscombe lifted the Junior World Cup with New Zealand in 2010 but is well aware there are plenty of big names, such as Dan Carter, Aaron Cruden, Beauden Barrett and Tom Taylor ahead of him for the All Blacks.
Now he can follow the likes of New Zealanders Sonny Parker, Shane Howarth, Brett Sinkinson, Matt Cardy, Hemi Taylor, Dale McIntosh to wear the red of Wales.
Cardiff Blues would lead the chase for his services given they are set to agree terms with former All Blacks hooker Mark Hammett to take over as director of rugby.
Gatland said: “Gareth is probably fifth or sixth in the pecking order in New Zealand. He’s had a few chances recently because of Cruden’s injury but the beauty is that he plays both 10 and 15 and is also a good goal-kicker. It could be interesting.
“I told him that we would be keen for him to come to Wales, but there was no pressure.
“He is only 22 so whether he made that decision in three or four years’ time, there is still plenty of time. But my warning was to not get selected for New Zealand Sevens which would rule him out of being selected by another country.”
Anscombe would battle with Dan Biggar, Rhys Priestland and James Hook for the No.10 jersey.
Biggar, named Pro12 Player of the Season, is set to go head-to-head with former mentor Hook in the Wales trial at the Liberty Stadium this month with Rhys Priestland ruled out of the tour to South Africa with a knee injury.
Hook is set to leave Perpignan following relegation from the Top 14 with Lyon leading the chase.
But Gatland said: “We are uncertain over his future next season but we want James to come back to Wales.”
MATT LLOYD