The 39-year-old moved to Upton Park from Bolton Wanderers in 2012 and has served as both number one and a back-up to Adrian during his time at West Ham.
He is now under contract for a third season with the club and the former Finland international is eager to challenge for the No.1 jersey in West Ham's starting XI next term.
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"Hopefully I can put in a proper challenge to get a starting place again. Physically, I feel good now and I felt good last season so I hope I can carry on from there and play football.
"You never know what is going to happen next season, but the only thing in my mind is to get myself ready to play.
"I am looking forward so that when that next chance comes, I will be in the right shape and right frame of mind to take it. That's all I'm thinking about now.
"Obviously we all know that, whoever is in the squad, we all want to fight for that starting place, so let's see. We're all looking forward to next season.
"I want to try my best and I'm going to give it a proper go to play well, so the first thing I have to do is look after myself to make sure I'm in good shape and a good frame of mind."
Jaaskelainen made 18 appearances in the Premier League for West Ham last season, conceding 24 goals and keeping eight clean sheets.