For small areas with NoData I would go for the solution provided by Jayanta Poddar (but using the two steps in a single raster calculator expression). For larger areas in the past I have used a procedure to:
- detect the NoData Areas
- expand the NoData Areas
- use the expanded raster to get the border with values of the DEM
- convert that raster into points
- create a TIN
- convert to raster and replace the NoData values with the TIN 2 raster result
However, these are a lot of steps and what is most important, if you have a large area of NoData values, you probably don't know what happens there and any method will assume things that may not be true.