The veteran right-back's contract is due to expire at the end of the campaign, and according to James Benge of the Evening Standard, the Irons are considering taking advantage of the situation. West Ham boss Slaven Bilic is said to see the France international as a "short-term solution for a problem position."
According to Benge, Manchester City boss Pep Guardiola has not offered a new contract to the 34-year-old, as he's keen to add youth to his ageing defence.
Indeed, the full-back positions at the Etihad Stadium could do with some freshening up. At right-back, Pablo Zabaleta and Sagna are the only two natural options, while on the other flank, Guardiola has Gael Clichy and Aleksandar Kolarov to call on; at 31, Clichy is the youngest of that quartet.
Although he doesn't raid down the flank with the kind of endeavour he did in his Arsenal days, Sagna still possesses quality, as Sachin Nakrani of The Guardian noted earlier in the season:
West Ham have been using Cheikhou Kouyate as a right-back as of late, with Sam Byram suffering with a succession of injuries and Alvaro Arbeloa struggling to make an impact. As such, it would make sense for the Irons to snap someone of Sagna's experience up.
The Frenchman has made 14 appearances for City this season and has acquitted himself well in the main, picking up one assist. With regular football at somewhere like the London Stadium next season, he could still do a fine job at the highest level for a while yet.
City in for Dani Alves
The City manager worked alongside Alves to great effect during a spell together at Barcelona, with Alves' blistering surges on the right flank a crucial part of their attacking plan. Guardiola is said to be keen to add the 33-year-old's experience to his squad.
Alves ended his memorable spell at Barcelona in the summer, moving to Turin for a new challenge with the Italian champions.
Here's a look at some of his standout moments so far:
In truth, positive moments have been rare for Alves since his move to Juventus. He's made 14 Serie A appearances, although he has not been able to offer the threat in the final third that made him such a big hit at the Camp Nou.
However, having recovered from injury problems and cemented his place in the team, there are signs that he's beginning to adapt to life under manager Massimiliano Allegri and his manager to him, per David Amoyal of ESPN FC:
Of course, Alves is not the trailblazing right-back who thrived under Guardiola in Catalonia any more. His advancing years mean he has to be smarter when picking his forays forward, although his quality on the ball and winning mentality would be enough to make him an asset at the Etihad Stadium.
His arrival would need to be supplemented with another long-term acquisition at right-back, though. As aforementioned, City's back four has looked a little tired at times this term and needs a dash of dynamism before the start of the 2017-18 season.