Sebastian Vettel has again emerged as Red Bull's leading driver this season, claiming two race victories – by means fair or foul – while Webber has yet to get off the mark.
As such the German is leading the Drivers' Championship on 89 points with Webber is sixth place having bagged less than half his teammate's points.
It remains to be seen whether this season will be 36-year-old Webber's last in Formula One as the Malaysian GP controversy put a damper on his relationship with Vettel and the team.
However, it may not be Webber's choice as to whether he goes or not as Horner says the next few races could decide his future.
Asked by Sky Sports News if the upcoming races were a "period of opportunity or one of additional pressure" for Webber, his team boss said: "It's probably both.
"At the end of the day there is pressure to perform, but that exists for all the drivers. Monaco is a circuit that Mark in particular enjoys and excels at so hopefully he can have a very strong run there."
Horner, though, insists it is still too early to talk about his potential 2014 driver line-up as the season is just five races old.
"We're only five races in and just a quarter of the season through this Championship," he added.
"Our decisions regarding drivers will be made in the summer and Mark, if he's delivering and motivated and has the desire to continue, of course [as] a driver that we know and achieved so much with us we'll consider very, very closely.
"But no decisions will be made about drivers until later in the summer." Planet F1