The Russian businessman sent McDermott messages of support after Tuesday's 3-0 defeat at Sunderland.
It was Reading's fifth straight loss in the Premier League leaving them marooned in the relegation zone, six points from safety.
McDermott is now the bookies' favourite to be the next managerial casualty in the Premier League.
But the 51-year-old has the full support of Russian businessman Zingarevich.
"Anton sent me a fantastic text on Tuesday," revealed McDermott. "He said he understood exactly the situation we are in and I appreciate that support.
"Yes, this is a big challenge for us. We haven't had the rub of the green and we are down to the bare bones with injuries. But all we can do is be ready for the next game against Arsenal and do our best."
Reading spent a meagre £5 million transfer fees last summer and the lack of investment appears to be catching up with them.
But Zingarevich is now ready to back McDermott in the January transfer market following links with Russian duo Roman Pavlyuchenko and Andrey Arshavin.
McDermott is also said to be interested in signing out-of-favour Stoke City midfielder Wilson Palacios and Nottingham Forest keeper Lee Camp.
Royals boss is now set to sit down with Zingarevich this weekend to discuss the way forward.
"I think Anton is leaning more and more about this division," added McDermott. "We know where we are in the pecking order, we've just got to keep going.
"I think last summer we needed to bring in a bit more than what we did.
"My gut feeling is we need Premier League players who have done it at this level. We will do our best to find them.
"I'm not sure who is available but we will look to strengthen.
"I will be meeting with Anton this weekend to discuss things further then we will go from there."