"We are much happier that it is up to us now," Hodgson told a news conference ahead of Saturday's visit of Leicester City.
"Having pulled ourselves out of the bottom three, it is important that we stay out of there... 38 points would seem to be a good total this year, with so many teams not close to that.
"As far as we are concerned, we try to win all three matches and take no chances. I won't be relaxing until we are mathematically safe."
The Football Association (FA) have held talks to sell Wembley Stadium, the home of the England national team, to U.S. billionaire Shahid Khan in a deal that British media said could be worth up to 1 billion pounds.
The deal could force England to play away from Wembley but Hodgson, who managed the national team between 2012 and 2016, has backed the FA's decision.
"I think that if the FA have made a deal, it will be for the right reasons," Hodgson added. "And that money would be spent in the right way to help our football in England.
"I enjoyed Wembley like managers before me and I would be disappointed if that was the end of England at Wembley, but I don’t think that will be the case. If a couple of games are taken around the country, I don’t see that as a negative."
Hodgson said striker Connor Wickham has returned to training having been out since rupturing his cruciate ligament against Swansea City in November 2016.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
