According to Mundo Deportivo, the La Liga giants will activate Seri's €40m (£36.5m, $47m) release clause and it is thought that he will become a Barcelona player next week.
The Ivory Coast international is viewed as a viable alternative to chief summer target Marco Verratti, who looks set to remain alongside Neymar at Paris Saint-Germain.
However, MD stress that his arrival does not prevent Los Cules from continuing their pursuit of Philippe Coutinho.
If a deal is completed as expected, then Seri will follow Marlon Santos, Gerard Deulofeu, Nelson Semedo and Paulinho as Barcelona's fifth signing of the summer transfer window to date.
The Catalans, who netted an eye-watering €222m from Neymar's world-record move to France, have failed with two lucrative bids for wantaway Brazilian playmaker Coutinho and are said to have set a deadline for a final response on a third offer worth in the region of £114m.
They also remain firmly on the trail of talented young French forward Ousmane Dembele, although a scathing Borussia Dortmund are adamant that they will not sell for anything less than the asking price. Barcelona could turn to former Real Madrid star Angel Di Maria as a potential Plan B in the event that they do not succeed in that particular pursuit.
Seri featured for the entirety of Nice's 2-0 Ligue 1 victory over Guingamp at the Allianz Riviera on Saturday (19 August) and manager Lucien Favre appeared to possess little knowledge of any imminent departure. Ajax conquerors Les Aiglons host Serie A contenders Napoli in the second leg of their Champions League play-off round tie on Tuesday evening.
"Are you serious? I can not imagine life without Seri," Favre told reporters, as per Marca. "But while the market is not finished, just as it is at many other clubs, everything is unknown. He has been very professional in all of our games. I cannot tell you anything else, I know nothing at all."
Seri, who joined Nice from Portuguese side Pacos de Ferreira in 2015, has attracted interest from a multitude of clubs following a highly impressive second campaign in the French Riviera in which he scored seven goals and registered nine assists to help Favre's men finish third in Ligue 1. He also saw off competition from Ryad Boudebouz and Benjamin Moukandjo to win the 2017 Prix Marc-Vivien Foe award for the league's best African player.
Barcelona have been understandably keen to bolster their midfield this summer as doubts continue to surround the status of Nou Camp stalwart Andres Iniesta, who admitted on Sunday that he has still yet to agree a contract extension. The 33-year-old's current deal is due to expire in June 2018 and he admits he is now pondering his future.
"In fact, I have not yet renewed [my contract]," he told El Pais. "I have experienced many sensations that I did not know, but I think they are normal. It is a scenario that three years ago I surely could never have imagined. Let's say, I'm thinking about the future when I did not do it before."