Miller is looking for a new club after being released by the Millers at the end of last season, but there is no shortage of interested parties.
He has held talks with Plymouth, Fleetwood and Burton while Lincoln and Cambridge are also keen on signing the 26-year-old.
And now it is understood Pompey have also expressed an interest.
The two parties are yet to formally discuss a deal, but it is a move that Miller would be keen on.
The south coast club, under boss Danny Cowley, are building a squad that is capable of launching a League One promotion bid and Miller is a player who knows what it takes, having been part of the Rotherham squad that finished second last season.
Miller was a key player for large periods of the season in a left wing-back role but injuries ruined the second half of the campaign.
Despite his impressive performances, boss Paul Warne opted not to offer a fresh contract, leaving Miller a free agent.
Joe Mattock was also released after seven years at the Millers and he has joined League Two side Harrogate Town.
The 32-year-old was hugely popular at the AESEAL New York Stadium but suffered regular injuries over the last couple of years.
Mattock said on Instagram: “I just wanna say a big thank you to everyone @officialrufc for my time there, I’ve had some unbelievable highs and it’s honestly been the best 7 years of my life! “But my time has finished there now and it’s time for a new chapter @harrogatetownafc.”