Q.New leaves are growing from a bouquet of roses, can the roses be rooted successfully?
Recently, I was given a bouquet of roses and as the flowers opened and dried up, I noticed most of the stems had new leaves emerging. I do not see any roots developing in the vase. Can I try to root the stems? Each day, more leaves are emerging and I would love to try to save the roses by potting them.

I'm not sure of how successful rooting these cut roses will be, but there is no harm in trying! Follow the propagation directions in this link and good luck!
https://www.gardeningknowhow.com/ornamental/flowers/roses/roses-from-cuttings.htm