Owen is available on a free transfer as his contract with Manchester United expired at the end of the season.
Cottee said: “West Ham need to make three or four new signings — and Owen would fit the bill. A new striker is a must but also a proven Premier League scorer would be ideal.
“Everyone talks about Owen’s injury record but you know he guarantees reaching double figures in goals which would take so much pressure off the rest of the players.
“I know the fans would be excited about signing someone of his calibre. It would send out a message the board want to back the manager with quality.”