The Hammers are looking to build a squad capable of competing in Europe and also maintaining the level which saw them finish sixth in the Premier League last season.
Moyes is keen to add a striker to provide support and competition for Michail Antonio, the only senior centre forward in the squad, though a central defender is the main priority.
West Ham remain in talks with Fiorentina over a £14million deal for defender Nikola Milenkovic and are hopeful of a breakthrough this week.
A move for Chelsea centre-back Kurt Zouma collapsed earlier in the window but tentative negotiations have been reopened over a potential move for the Frenchman.
West Ham’s only signing so far this summer has been goalkeeper Alphonse Areola on loan.
“We always want competition and I am always looking to see what options there are,” Moyes said.
”I am hoping by the end of the window we might have some more additions but I can’t guarantee anything. There is a long way to go in the window yet.
“We’ve improved in the goalkeeping area, we thought it was something we’d like to do. Good competition, I think most people saw how well Areola did at Fulham last season.
“I hope that he’ll give us competition there. I want to make sure that we do have competition and I’m hoping we do by the end of the transfer window.”