Deshaies has spent the past 15 years in the Astros television booth following a 10-year playing career, including seven seasons in Houston.
Brenly left the position after eight seasons in the booth with play-by-play man Len Kasper. He took a similar role with the Arizona Diamondbacks when negotiations on a four-year contract unraveled in early October.
The Cubs interviewed several candidates, including MLB Network analyst Dan Plesac and Fox studio analyst Eric Karros, industry sources told ESPNChicago.com's Bruce Levine. Both are former Cubs players.
The contracts for Cub baseball broadcasters has been handled by WGN since they began broadcasting Cubs games in 1948. The Cubs broadcast 65 to 70 games on WGN which used to carry upwards of 154 per season until the partnership between the Cubs, White Sox, Blackhawks and Bulls was formed with Comcast a decade ago.
The left-handed Deshaies was 84-95 during stops with the Astros, San Diego Padres, Minnesota Twins, San Francisco Giants and Philadelphia Phillies. His best season was with Houston in 1989 when he went 15-10 with a 2.91 ERA.