The 37-year-old’s current contract with Bolton is set to expire at the end of the season.
Jaaskelainen is reportedly ready to leave Bolton if they are relegated.
West Ham boss Sam Allardyce, who worked with Jaaskelainen at Bolton, is reportedly keen on signing the Finn, but face competition from West Brom.
A friend of Jaaskelainen told the Daily Star: “If Robert Green goes, there’s the obvious connection with Sam and Jussi is also on West Brom’s list.
“If Bolton don’t go down, Jussi will probably sign the new deal but if they are relegated then he’ll probably leave.”
