The veteran goalkeeper will be 39 by the time his current deal is up, but he has no intention of hanging up his gloves.
Jaaskelainen remains Sam Allardyce's number one at Upton Park and is one of the Premier League's most consistent shot-stoppers.
He hopes he will be offered the opportunity to prolong his career in the English top flight, with it his intention to earn fresh terms by maintaining his high standards.
Jaaskelainen told the Hammers' official website: "My contract is until the end of the season and that's what my aim is at the moment. But I want to go on as long as I can.
"The goalkeeping coach and backroom staff are fantastic and look after me pretty well.
"They know my needs and give me one or two extra days off now and then.
"Experience as a goalkeeper is important and the main aim is to be consistent."
Jaaskelainen also credits Allardyce - a man he worked with at Bolton Wanderers before reuniting at Upton Park - with helping to prolong his playing days.
He added: "I like to work with Big Sam and like the way he has brought science to the game.
"When I joined him at Bolton we were a Championship side, and he hired peopled to make sure we were looking after ourselves and preparing properly for the match on a Saturday."