The Daily Express are reporting that Championship winners Hearts have indicated an interest in the 24-year-old, who is out of contract in the Highland capital at the end of the season.
Neilson is believed to be keen on striking a deal that would bring the former non-league footballer to Tynecastle during the summer.
Watkins looks almost certain to leave Inverness, who he joined in 2013.
However, Hearts face competition from a number of clubs, with English Championship side Blackpool and Polish outfit Slask Wroclaw also monitoring Watkins.
Watkins has played 62 games for Inverness CT in all competitions, scoring nine goals in the process.
He had spent most of his career in the English non-leagues after a three-year spell with Cheltenham Town yielded just 26 outings and a solitary goal.
He played 61 matches for Bath City including a loan spell, and netted eight times.
A season with Hereford United saw Watkins score five goals in 35 appearances before being tempted north to sign for the Caley Jags.
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