Gooden is to be released from a Gainesville, Fla., prison Thursday after finishing a sentence for violating his probation by using cocaine.
"I haven't spoken or seen Dwight Gooden, but I'll always have room to talk to him," Steinbrenner said in a statement to the New York Daily News.
"I want to see what his plans are and what his hopes are, and then I'll be able to relate to that and determine what, if anything, I do."
Gooden, 41, was arrested in March after he acknowledged to his probation officer that he had used cocaine.
He entered prison April 17 and served seven months of a year-and-a-day sentence.