The Star understands the Owls have had an offer rejected for the Frenchman, who can operate in defence, on the wing or up front.
Mohsni, who has spent two seasons with the Shrimpers, making 71 appearances, has missed the start of the club’s pre-season training.
A Southend club spokesman says Mohsni has been allowed to come back into the first-team squad “a bit later” because of a family wedding in France.
Wednesday boss Dave Jones, who has yet to taste defeat since replacing Gary Megson at the helm in March, had admitted he has inquired about Mohsni’s services.
The highly-rated 24-year-old has a year left to run of his contract at Roots Hall.
Jones has completed his sixth summer signing yesterday by snapping up Portuguese midfielder Diogo Amado on a free transfer from Uniao Leiria.
The 22-year-old has penned a two-year deal at Hillsborough, subject to international clearance, having been recommended by current Owls player Jose Semedo, who knows Amado from his former club, Sporting Lisbon.
Amado said: “I am incredibly excited about this move. I know Sheffield Wednesday from Portugal and it is a big, big club.”
Former Owls striker Deon Burton is on trial at MK Dons after departing Gabala in Azerbaijan.