The former champions announced in July they had signed Key from Red Bull-owned rivals Toro Rosso, who signalled they would not be letting him go without a fight.
"James Key has a long term valid contract with the team," Toro Rosso boss Franz Tost said at the time.
McLaren principal Zak Brown told reporters at the Italian Grand Prix that a start date had yet to be determined.
"I think it’s highly unlikely he will join us this season," added the American.
"I wouldn’t expect James to have any impact on our 2019 car. We are already aware and working accordingly.
"Ideally you would have James involved but this is going to take some time to rebuild the racing team," continued Brown. "We probably won’t be at our full capacity of technical capability until our 2020 car."
Previous technical head Tim Goss was moved aside in April, after former engineering director Matt Morris resigned. McLaren also parted company with Racing Director Eric Boullier in July.
Double world champion Fernando Alonso is leaving the sport at the end of the season, and his Belgian team mate Stoffel Vandoorne could follow him out of the door to leave a clean slate on the driver side.
McLaren, sixth in the standings, have endured another poor season after three nightmare years with Honda.
They blamed that period largely on the under-performing and unreliable engine before having to recognise this season, with a switch to Renault, that their chassis was not good enough either.
Brown was confident McLaren, the second most successful team of all time who this year celebrated the 50th anniversary of their first race win, would have a better car next year and accepted 2018 had been a disappointment.
"I think other teams have developed at a faster pace than ourselves. It appears that we’ve gone backwards," he said.
"I think everyone else has gone forwards but in Formula One if you’re not going forwards, you’re going backwards."
The American said Belgium and Italy, both high-speed circuits, highlighted the car's failings more than other tracks but the team would not give up development.
"We will continue to push on this car but unfortunately we’ve produced an extremely poor race car that is not that responsive to changes," he said.
(Reporting by Alan Baldwin, editing by Toby Davis)
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