Sunderland saw a host of players depart the Stadium of Light at the end of last season after the club pulled off a great escape to ensure Premier League survival.
Thus far, last term's League Cup runners-up have added four players to their first team squad with goalkeeper Costel Pantilimon, full-backs Patrick van Aanholt and Billy Jones and midfielder Jordi Gomez penning deals at the club.
However, head coach Poyet is keen to acquire further additions and has urged the club to press on with signing four more players by next Wednesday so he has enough time to work with a completed squad before the league opener at West Brom on August 16.
"One or two they are close, but if you had asked me last week I would have said those two were close too," Poyet said after Sunderland's 1-0 friendly win over Recreativo de Huelva on Tuesday.
"I cannot wait another week. We are going to be off Monday and Tuesday, so next Wednesday I need to have four new players.
"It's clear we need a few new players, and it has not been as quick as I would have expected.
"It's getting a little close to the part where I really want to work with the main squad.
"I am like any other manager, the sooner you get the players the better. I hope it is now, today, tomorrow.
"It's difficult for me because there are things we need to work on this week, and the beginning of next week and that's practically it.
"The only thing you can do [in the last week of pre-season] is ensure everything is in place and refresh things that you've done."
