Quarterback Eli Manning had a 27-pick campaign in 2013, but he made it through to the bye week with just five interceptions.
"I just think, as an offense, we have to be more aggressive," Reese said, NFL.com reports.
"I think at times we're a little bit almost too cautious with what we're doing offensively. This is the National Football League. You've got to go out there and you have to win the game."
Manning will be heading into the final year of his contract next season but Reese was adamant that no discussions will take place until the end of the current campaign.