The 30-year-old former Scotland international was sidelined for 18 months after breaking his foot in a challenge with Tottenham full-back Pascal Chimbonda.
He made his comeback last season during loan spells at promoted Championship duo Birmingham and Wolves and is now back at Upton Park ahead of the new Premier League season.
Quashie knows he will find it tough to force his way into Gianfranco Zola's plans, but is just happy to be able to be involved with the Hammers.
He told skysports.com: "A lot of players have been brought in to the club since I picked up my injury and it's always going to be more difficult for me to get back into contention for a first-team place because I have been out for so long.
"I understand the position that I am in, but I'm not worried about that because it's a relief for me just to be fit again and able to go out and play football.
"At one stage I seriously considered packing it in because I didn't think I would be able to get back to the same level that I was at."
And Quashie does not fear his injury woes returning after suffering no setbacks during his stints with Blues and Wolves.
He added: "I've got no concerns about it now because I've come through the games at Birmingham and Wolves and it has stood up to the tests that have been thrown at it during both the games and everyday training exercises.
"I've got an opportunity to go on and play for another couple of years and I intend to enjoy playing football for as long as I can.
"My spell at Birmingham was brilliant for me and Alex McCleish was first class in helping me to regain my fitness and get some games under my belt.
"Wolves was a little different because they were flying and I knew that I was brought in to help the younger lads get over the finish line, but it still helped me because I was training with the lads there every day."