Slaven Bilic's side have enjoyed a strong start to the season and the fans are dreaming of Europe.
The Hammers had started the season strongly, with big wins away against Arsenal, Liverpool, and Manchester City under their belt.
That had fans dreaming of a potential push for the top four, with those places very much up for grabs given the open nature of the Premier League this season.
However, they have fallen away in recent weeks with several disappointing displays, and Cottee says he would be more than happy with a top 10 finish from Slaven Bilic’s side.
“There has been talk of challenging for a European place but, for me, the bigger picture is finishing in the top half of the Premier League table,” he told whufc.com.
“We made a sensational start with the away performances and wins at some of the top clubs but I still think that if we get the results to get a top nine or ten finish I will be absolutely delighted.”
“The main priority is that we are still a Premier League club when we move into the new Stadium next summer.”
While Cottee says that a top 10 finish is a more realistic target for the Hammers this season, there is no denying that they are firmly in the race for Europe at present.
They are currently eighth in the table with 22 points, a tally that leaves them just one point short of Liverpool in sixth place.
Beyond that, though, they are also within touching distance of London rivals Arsenal, who currently sit fourth in the table on 27 points, just five points away.