The 26-year-old Liverpool-born runs out of contract at the end of the season and is keen on moving on after indicating he won’t be extending his deal at the Priestfield Stadium.
Eaves currently tops League One’s goalscoring charts with 13 goals in 19 games, and is on course to beat his last season’s tally of 17 goals in 41 games.
Rangers are in dire need of reinforcements in the striking department after AS Roma’s Sadiq Umar failed to impress upon arriving Ibrox on loan at the beginning of the campaign.
Eaves looks like a perfect replacement for the Nigerian flop and competition for his signature could be fierce this winter.
Rangers have scored 38 league goals in 15 games under manager Steven Gerrard – the most in the Scottish Premiership – but they still have to do more if they are to have a chance of challenging Celtic.
Striking duo Alfredo Morelos and Kyle Lafferty remain reliable sources of goals, but Eaves can bring much-needed competition and cover to the squad if snapped up.