Assuming you have the mouse plugin added.
mouse.x, mouse.y give actual position.
Which isn't what you are asking for, but it would be smooth.
try:
every tick
set the sprite to position
Tilemap.PositionToTileX(Mouse.X)*Tilemap.TileWidth
Tilemap.PositionToTileY(Mouse.Y)*Tilemap.TileHeight
It'll be choppy movement, but I believe that's what you're wanting.