Quoting both of the spells, Sleep (PHB p.276) states:
(...) each creature affected by this spell falls unconscious until the spell ends, the sleeper takes damage, or someone uses an action to shake or slap the sleeper awake.
And Entangle (PHB p.238):
Grasping weeds and vines sprout from the ground in a 20-foot square starting from a point within range. For the duration, these plants turn the ground in the area into difficult terrain.
A creature in the area when you cast the spell must succeed on a Strength saving throw or be restrained by the entangling plants until the spell ends. A creature restrained by the plants can use its action to make a Strength check against your spell save DC. On a success, it frees itself
When the spell ends, the conjured plants wilt away.
So by the spell description, Entangle doesn't cause any damage to the affected creatures, which makes me think it wouldn't wake creatures affected by Sleep spell.
Moreover, unconscious creatures automatically fail their Strength Saving Throws (PHB 292), so they get automatically entangled as well.
Do these entangling vines affect the asleep creatures in any way so they wake up?