I am dealing with Landsat 8 images, it has some gaps in the images without any data. I am wondering is it possible to use ArcGIS to fill these gaps, instead of ENVI?
If the 'gap' means an area without data, the only way to 'fill' is to find another data source, then a mosaic can be compiled in any GIS software environment, ArcGIS, ENVI, whatever. If the 'gap' is a 'no-data part at the edge of the image' and another Landsat image contains its data, then the image should be cropped, omitting the 'no-data frame'. Again, it can be done by any GIS software. However, I repeat, no software can produce data, which are not in your source images.
If you have a multitemporal dataset (more images of the same region over time) more possibilities open up to perform gapfilling. But if you have only one image with gaps, then you will have to apply the approach as suggested by Gabor Timar.
The answer depends upon the nature of the data. As Gabor said, " no software can produce data". However, if there are complimentary information available, you could try.
The question comes back to what kind of data do you have. Is it one image or do you have multiple images (time series)?