The two clubs had agreed a fee for the 25-year-old, who has scored 13 goals in 44 games for City but has not been a regular in their first eleven.
Showunmi has decided to remain at Ashton Gate and fight for his place in the team.
Showunmi joined City from Luton in 2006 on a Bosman free transfer having helped the Hatters win back-to-back promotions from League Two to the Championship.
The twice-capped Nigerian international has made 17 appearances since the start of the campaign, but City boss Gary Johnson is believed to have been told he must sell before the board at Ashton Gate will sanction new signings.