David Moyes wants West Ham fans to give him some "breathing space" to build on their success this season.
Moyes is understood to be on the brink of signing a new three-year contract at the London Stadium.
The 58-year-old Scot guided the Hammers into the Europa League after breaking the club's record Premier League points tally and finishing sixth.
Former Everton boss Moyes had previously twice saved West Ham from relegation, having been parachuted back in for a second spell in charge in December 2019.
West Ham fans have not always been onside with the club's hierarchy, particularly following the move from Upton Park to the former Olympic Stadium, but Moyes has helped build some bridges this season.
He told TalkSport: "If I was a West Ham supporter and David Moyes had come in and saved us from relegation once, came in and saved us from relegation twice, and then in the first full season qualified for Europe, I'd be hoping you would give him a bit of breathing space.
"Even at Everton I couldn't get them into Europe in the first year, so it has been a huge step. I would hope West Ham supporters are going to say 'we're going to give him an opportunity to build on it'.
"Am I going to push the team more? Yes, but we've taken an almighty step. Quite often you have to take a step back and go again but at Everton we were around the top eight most seasons.
"There is so much room for growth at West Ham."
