Cummings, 25, has struggled to hold down a regular place in Royals’ first-team, and manager Steve Clarke could let him go for the right price.
Clarke has a number of options in the full-back position with Chris Gunter, Stephen Kelly, Jordan Obita and youngster Jack Stacey all comfortable in the role.
Ex-Chelsea trainee Cummings made six league and cup appearances during a promising start to the season under former boss Nigel Adkins.
He then picked up a knee injury and had to wait another three months for his next appearance in the 2-2 draw at Brighton on Boxing Day when he replaced Jake Taylor on the hour mark.
Reports now suggest Millwall and involved in discussions with Royals over a transfer fee.
The Lions are also poised to sign former Reading striker Simon Church from Charlton Athletic on loan for the rest of the campaign.
But Clarke has suggested Royals may not be in a position to do any business in January due to Financial Fair Play rules.
It leaves Clarke short of options up front after his chances of signing on-loan striker Glenn Murray on a permanent deal were scuppered this week.
The 31-year-old netted eight goals in 18 appearances for Royals, but is now back with Crystal Palace and is rumoured to be close to penning a new contract after being given a second chance by new Eagles boss and former Reading manager Alan Pardew.
Murray featured for Palace in their FA Cup win against Dover last weekend and he could be involved in their Premier League fixture against Tottenham this Saturday.
Clarke is likely to ask Nick Blackman to fill the void up front alongside Simon Cox, with winger Hal Robson-Kanu and youngster Dominic Samuel his only other viable options in attack, with Pavel Pogrebnyak sidelined through injury.
Clarke will be searching for his third successive victory in all competitions this Saturday when Royals host Middlesbrough in the Championship at Madejski Stadium (3pm ko).
Blackman, who came off the bench to score the only goal in the 1-0 FA Cup win at Huddersfield last weekend, could make his first start since the 3-1 league defeat at Blackburn on November 1.
Meanwhile, Reading flop Royston Drenthe looks set to seal a permanent switch to an unnamed club in China, having spent the early part of the season on loan at Sheffield Wednesday.
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