Colombia international Muriel has scored 21 Serie A goals for Samp in 76 appearances since his arrival from Udinese in 2015, including 11 in the campaign just gone.
And, with the 2018 World Cup on the horizon, the 26-year-old could look to make a higher profile European move so as to stake his claim to a spot in the team, and potentially the first eleven.
Indeed, he will have to vie with established stars Radamel Falcao, Carlos Bacca and Jackson Martinez, with the latter eyeing a European return following a torrid spell in China.
And regardless of the new deal, after two seasons with the Genoa based club, Muriel has admitted his future is uncertain.
He told ESPN: “There are a lot of rumours about me and my agent told me he will only call with something concrete.
“In the meanwhile, I’m calm, I renewed with Sampdoria and I’m not thinking much about what might happen.”
Hammers boss Slaven Bilic has made signing a striker his top priority this summer, with versatile midfielder Michail Antonio topping the club's scoring charts with nine last term.
With Jonathan Calleri returning to Boca Juniors after a disappointing loan, and Andy Carroll and Diafra Sakho injury prone, there is indeed a glaring need to rejuvination up top.
However, the club will be wary in their dealings with Serie A clubs, having brought Simone Zaza from Juventus last summer and seen him fail so spectacularly.