Spurs are two points above 18th-placed West Ham going into the last matchday. West Ham, who have a significantly worse goal difference than Spurs, need to beat Leeds United on Sunday and hope for Spurs to lose to Everton to avoid the drop.
A draw with Everton will likely be enough for Spurs to avoid relegation.
"I'd love to keep West Ham in the league if I can," Moyes told reporters on Friday.
Moyes spent five-and-a-half years as the West Ham manager in two different stints between 2017 and 2024, and helped them win the UEFA Conference League in 2023.
But the 63-year-old was quick to clarify that his primary focus on Sunday will be to help Everton finish higher, with a top-10 finish still possible for the club.
"It's more important I get Everton that top finish and we get a few more million pounds because of our league position," he said.
Spurs, who dug themselves out of the bottom three under new manager Roberto de Zerbi, have lost only one of their last five matches, while Everton are on a six-match winless streak.