Eric Boullier is expecting "massive progress" from McLaren-Honda but concedes it is still too early to predict where they will be in the pecking order.
Unlike at the beginning of 2015, this year McLaren's pre-season has looked a great deal more promising.
McLaren managed to rack up the laps on all but the last day, bringing their tally for the four-day outing to 257 laps, a notable improvement on the 79 they covered in last year's first outing.
And although speed was not on display – Fernando Alonso was P18 and Jenson Button P22 of the 23 drivers – there were signs of encouragement.
"We can’t say any numbers – it’s still too early," Racing Director Boullier said in interview with the official F1 website.
"But we are making big improvements and making massive progress. And there will be massive progress this year.
"The fact that there is more freedom for the engine manufacturers will have an impact, as you are able to change your targets and your timing.
"I definitely don’t want to build any wrong expectations – that would be wrong for everybody, including the drivers."
He did, however, add that for 2016 the story may not end with 'and they all lived happily ever after'.
"Ha! Not really – because for that we would have to win the championship!" he stated. "This 'happily ever after' is a bit early days. But it will come!"
The Frenchman also revealed that it wasn't only Honda who had produced a better product over the winter but also McLaren.
According to Boullier, the new MP4-31 is a "huge evolution" that goes a long way towards resolving its predecessor's weaknesses.
He said: "As far as McLaren is concerned we’ve been working very hard on the huge evolution of the car. We left no stone unturned.
"The car from last year has been really stripped down to details and we’ve tried to correct any weaknesses and it looks positive on the first test analysis.
"We have really improved the car itself. And we want an engine that matches that."