If you mean both of you have already got mono,the answer is no,because the virus is life-long and the antibodiies also remain almost always forecer.But just if there is a slump in the immune system caused by a reason as HIV or other immune desease-the reactivation of the virus is possible but this does not matter whether there is a contact because you will have this virus then so safe yourself from HIV,you know how,by using a condom with other sex partner or better do not have
I'd love to know other thing-if mono can be transmited via small droplets in the air when talking and after that directly either being swallowed when talking with an open mouth, inhaled, or even contact with the eyes,as other saliva infections such as flu do pass .So is it possible to get EBV without kissing or sharing infected objects from mouth or nose ;just by doing nothing
I'm looking forward this answer very much because
some say it is but they tend to pose sneezing or coughing (but why not talking) and other do say not as an aerosol,that the transsmition requires just direct contact with saliva.