Typically, a mammalian cell contains between 10-30 picogram total RNA of which up-to 5% can be the mRNA. Thus, a cell can have between 0.5 to 1.5 pg mRNA (the upper limit).
To add on to Dr. Choubey's helpful response, a lot of useful numbers in biology can be searched in the Harvard Bionumbers database: http://bionumbers.hms.harvard.edu/