Hi Boris,
The basis is a Shrinkwrap Modifier. The problem is to make the transition from ‘unshrunk’, to ‘shrunk’, because the Shrinkwrap Modifier doesn’t have some thing like an Influence slider.
Maybe the simplest way, would be to Assign a Weight of 0 to all Vertices of the wrap (a Cylinder in this example) and change that over time to 1, with for instance a Vertex Weight Mix Modifier:

look at the Course Modify, for a refresher on the Shrinkwrap Modifier.