Guenther Steiner reckons Haas is set to receive Ferrari's engine upgrade, alongside Sauber, at next month's British Grand Prix.
Ferrari introduced an updated turbocharger at the Canadian Grand Prix, with Sebastian Vettel having finished second in successive races.
Steiner now expects Haas to be boosted by the upgrade when Formula 1 visits Silverstone in two weeks.
"We should get the engine upgrade in Silverstone," Steiner told the official F1 website.
"My information is that we get it at the same time as Sauber. And, of course, there are always new bits and pieces at pretty much every race.
"Of course, we also will shift our resources at some point to the 2017 car - but right now it is important for us to establish Haas in the pecking order."
Steiner's squad occupies eighth place in the standings and, despite failing to score points across the last four races, believes it has established itself firmly in the midfield.
"We are still mingling with the Force Indias, the Williams and the Toro Rossos," he said.
"And, of course, we want to stay there. I think we have gained the respect of everybody in the paddock - and that was another thing that we wanted to achieve. The worst thing would have been to become an embarrassment."