Sakho looks set to leave the Hammers as they search for a new top-class striker.
The Hammers are currently engaged in a high-profile search for a new top-class striker, with targets including Alexandre Lacazette and Carlos Bacca at the top of their shopping list.
Enner Valencia is also said to be closing on a move away from the Olympic Stadium, with Galatasaray reported to have agreed terms with the Ecuadorian.
However, whilst Slaven Bilic and the club's owners are hunting for a new hitman, Cottee believes that the solution to their problem would have been right under their nose if it were not for injury absences.
The Hammers legend told the Essex Chronicle: "The club needs a goalscorer. I was hoping that would have been resolved within. I was a fan of Sakho, if he could have stayed fit, then I think he could have got the goals last season.
"Andy [Carroll] was injured, Valencia was injured, everyone had their problems last year and yet the club finished seventh without any of the forwards getting 10 goals.
"A good goalscorer you've got to looking to scoring 15 Premier League goals, not 15 in all competitions and if West Ham can get someone who can do that, then they will be right up where they were last season and hopefully pushing on to where everyone at the club wants."
Sakho missed three months of the season at a hectic time in the schedule for West Ham after suffering a thigh injury at the end of November, an absence which robbed him of the chance to put together some momentum.
If he completes his move to the Baggies, the Hammers will be left with just Valencia, Andy Carroll, and young summer signing Ashley Fletcher as out-and-out strikers at the club.