Andy Serkis may not be concerned with being asked to return as Gollum anyway, since he appears confident Amazon is looking for a fresh and re-interpretive take on the Lord of the Rings series.
Serkis is logical in thinking Amazon would look to build its own stable characters and storylines, rather than solely piggybacking off the original films makes sense, although that wouldn’t necessarily mean characters from the main franchise can’t make a cameo or two.
Recent news about the show may suggest otherwise, however, as rumors have swirled that Amazon is looking to involve the franchise’s famed director Peter Jackson in some way, though his was reportedly one of many that have been contacted by Amazon, so perhaps Serkis is right on the money with his analysis.