The current group of tight ends on the roster include: Zach Miller, Khari Lee, Rob Housler, and Gannon Sinclair.
To that point, the Bears went after restricted free agent Josh Hill last week, and made a contract offer to bring him to Chicago. The Saints had the option of matching the offer, if they wanted to keep him in New Orleans, and on Friday, that's just what they decided to do.
The Saints are keeping Josh Hill, per source— Nick Underhill (@nick_underhill) March 25, 2016
This means the Bears will continue to monitor the market, and potentially look at a mid-round prospect in next month's NFL Draft. As it stands, Miller certainly earned a one-year extension after a revived 2015 season, and the team hopes he will be able to contribute the same this season, but they can't enter the season with Miller and Lee being the #1 and #2 guys on the depth chart.