The Hammers have already made eight new signings this summer.
West Ham manager Slaven Bilic before the game
The Hammers have had a busy summer, bringing in eight new players to date in their attempts to build on an impressive first season under Slaven Bilic.
They have been particularly determined to improve their forward options with Andre Ayew and Jonathan Calleri, as well as youngster Ashley Fletcher, all arriving at the club.
The squad is still short in some areas though, with the right-back position one that is particularly weak.
West Ham United's Andre Ayew receives medical attention before going off injured
Michail Antonio started there against Chelsea on Monday but was hauled off after giving away a penalty in an indifferent display.
And Cottee believes that they should be targeting another right-back and a goalscorer before the end of the transfer window.
“Two positions stand out for me, the right-back position and although they’ve got quite a few forwards, they still need a goalscorer,” he told Sky Sports.
West Ham's Michail Antonio looks dejected
It remains to be seen if West Ham will add more signings before the end of the transfer window.
After the injury to Ayew the striker position is certainly one that will be concerning Bilic, who will presumably want to avoid putting too much pressure on Andy Carroll.
Given their struggles in finding a forward for most of the summer, though, it is not likely to be an easy task to find one before the end of the month and they may have to make do with what is available.
West Ham's Andy Carroll