The centre-back, who featured for Watford last season, injured his hamstring in the Shrimpers pre-season friendly against Great Wakering Rovers on Friday.
But the 30-year-old is hopeful that he'll be able to recover quickly and impress manager Steve Tilson.
"Southend United remains my number one choice," Stepanov told the club's official website. "However, I understand that since the club needs a starting centre-back, they cannot make a decision based on the 35 minutes I managed to play.
"But I like the club and the town, which is really nice. Also I found that the level of football in League One is quite close to the Championship.
"Of course there is a difference in the ability of the players, but it is not overly-significant."