Moyes has made five signings already this summer but is looking to make further additions to his squad before the transfer window closes at the start of next month.
Depay has been linked with a move to a Premier League club, with Barcelona desperately needing to offload players and wages in order to register their new signings ahead of the start of the La Liga season.
But when asked whether the Hammers had made an offer for the Dutchman, Moyes said: “No it’s not us. If it is I don’t know about it, that’s for sure.”
Central midfield has also been seen as a key area for reinforcement, with the Hammers having missed out on new Everton signing Amadou Onana after being unwilling to meet his wage demands.
Reports have claimed the Hammers made a £25million offer to Sporting for Nunes and Moyes confirmed: "We’ve bid for him and the boy chose not to come.”
West Ham remain in talks with PSG over defender Thilo Kehrer but are yet to agree a fee or personal terms with the German international.
“We’re not any further forward with it at the moment but we are progressing,” Moyes said.