Ramsey joined the Gunners in 2008 in a £4.8m move from hometown club Cardiff City and is Arsenal's longest-serving player and scored the winning goals in the 2014 and 2017 FA Cup finals. "I think Bernd Leno can learn staying here [and training] with Petr Cech every day".
Watford started the better of the two teams, pressing the Gunners high up the pitch and making it uncomfortable for them to settle in the match.
If it seems that the Wales global is not going to sign a new deal, Arsenal could look to offload the midfielder for a fee in the January transfer window rather than risk losing him for nothing.
Alexandre Lacazette was closest to Cathcart for the opener but he turned provider for Mesut Ozil to make the points safe.
Cech was forced off just before the half-time whistle when he pulled a hamstring while taking a goal kick.
Leno had to come on for his Premier League debut moments before half-time after Cech limped off.
As things stand, Ramsey could leave Arsenal on a free transfer at the end of the season if the north Londoners are unable to tie him down to a new deal.
Emery's prediction appeared wide of the mark as Ramsey was anonymous before being substituted in the second half, a departure marked by a frustrted shake of the head from the Wales midfielder.
Emery's creaky rearguard was exposed again when Isaac Success sprinted clear and clipped his shot past Leno, only to see it hit the far post.
Two minutes later Iwobi was back at it again, dropping a pass on the path of Lacazette, who teed up Mesut Ozil for the match the victor.