The 42-year-old, whose testimonial match takes place in early May, was released at the end of last season following 10 years with the club.
A former Hull player, Goodison played more than 400 games for Tranmere, who are currently at the foot of the table and saw Micky Adams leave as manager earlier this week.
With just two games left in the season, things are not looking good for Tranmere, and Goodison told the Liverpool Echo: “I could have played this season, especially in this league.
“No disrespect to the players we have got here now, but I think I could have done a better job.
“If Ronnie Moore had still been manager at the end of last season, I would have had high hopes of being okay for another year. I think I could have carried on playing until I was 43 or 44.”
Tranmere have not won in the league since mid-March and have lost their last four games ahead of Saturday’s trip to Plymouth.