The Hammers are 18th in the table with one match remaining as relegation looms over the club this month.
Relegation would lead to an exodus of talent leaving the side, most likely including Bowen who is already being linked with several Premier League sides.
A move away seems inevitable for the England forward, who is too good for the Championship. However, speaking to Andy's Bet Club, Strachan revealed that Bowen could stick with the Hammers, even if it would be a gamble with his future.
“Jarrod Bowen could do a year in the Championship, but he's a top Premier League player. There is a strong bond there, but as a footballer, in particular, you want to be playing in Europe, and you want to be playing at the top clubs. You want to be up there.
“He's probably got three or four years left with it because he's got incredible pace. Does he take a gamble and stay a year? Does he take a gamble and stay six months and see where they are at that point? And again, the Championship, if you went back three or four years ago, it was a big step down. It's not so big now.
“The crowds and the atmosphere of these games now are very good, but it's not the Premier League. Leaving might not go down well with his father-in-law, but I just like watching him playing football.
“If he does move on, then West Ham, they'll struggle because he is the focal point. Fans look at him. Players look at him, going: ‘Come on, do something because we're not that great.’
“It must be a horrible feeling to have that pressure on you every game. To have everybody looking at you every game going, ‘You're the one guy that can save us.’
The 29-year-old remains the best player at the club and if relegation is confirmed, he is very unlikely to stick by the side, especially as he enters his 30’s in December.