The 29-year-old has impressed for the Baggies since joining the club from Lokomotiv Moscow last summer.
Italian giants Juventus are reportedly one of the clubs interested in the highly-rated striker.
“Every player will consider a bigger move because progression is very important,” Odemwingie told Sky Sports News.
“If you’re a footballer, going to a higher level is always the target, you always want to be at the highest.
“If a top-10 team in Europe offers any player a contract I think he will listen to it. If it comes and the club are happy I might give it a think.
“But, as I say, that’s not my priority, my head is here and I’m really happy, of course I will think twice because I’m performing here and I feel great.
“So, I might end up saying no to any offer that comes if I’m not sure that I’ll be as happy as I am at West Brom.”
Odemwingie has scored 14 goals in his debut Premier League season.
He added: “I knew it was a difficult league to play in. Still, though, I’m an ambitious person and I set myself a target of 15 (goals).
“At the beginning of the season that may have seemed too ambitious for your first season in the Premier League, but now I’m close to getting that.”
