The five include Roberto Ferrarini, the director of ship owner Costa Crociere's crisis unit, and Jacob Rusli Bin, the luxury liner's Indonesian helmsman, as well Captain Francesco Schettino's deputy and two other crew members.
The court in Grosseto in the central Tuscany region is expected to rule on the requests on Saturday.
Schettino, who is accused of multiple manslaughter and abandoning ship, is currently the only one standing trial for the deadly accident off Giglio island in Tuscany which left 32 people dead.
Should the court accept the plea bargains, the highest sentence would be two years and 10 months for the company executive Ferrarini. Manrico Giampedroni, the cabin service director, would face two years and six months in prison.
Schettino's deputy, Ciro Ambrosio, would get a year and 11 months, while the Indonesian helmsman would get a year and eight months and officer Silvia Coronica would get a year and six months.
Audio from the ship's black box revealed the chaos on the bridge on the night of the shipwreck, when Rusli Bin was steering the huge liner and Schettino had ordered a risky "salute" manoeuvre near the island.
In the recordings, when the crew realises the vessel is bearing down on rocks jutting out of the sea near Giglio, Schettino can be heard yelling "hard to port" while Ambrosio appears to yell "hard to starboard."
The helmsman, who did not speak English or Italian fluently, is heard asking "hard to starboard?"
By the time Schettino had repeated his order it was too late to right the Concordia's course.
The luxurious liner crashed into the Giglio rocks on the night of January 13th, 2012 with 4,229 people from 70 countries on board, keeling over and sparking a panicked and delayed evacuation which saw some people forced to throw themselves into the freezing sea.
Schettino has complained that he should not be the only one standing trial for the accident.
His lawyers on Wednesday requested a sentencing deal of three years and five months in prison for admitting responsibility.
Costa Crociere, the biggest cruise ship operator in Europe, has accepted limited responsibility as the employer of all the suspects and was ordered to
pay a fine of €1.0 million in a controversial decision by a judge in April.
On Thursday, the court admitted a new video as evidence in the trial. Prosecutors said the footage from surveillance cameras aboard the ship will
show what happened during the various stages of the disaster – from the crash, to the evacuation order and the ship's capsizing.
It is also expected to confirm exactly what time Schettino left the ship. He has been accused of heading for shore while terrified passengers were still trapped on board, but he insists he fell onto the roof of a lifeboat when the ship rolled and was carried to land against his will.
The Grosseto court set the next hearings in Schettino's trial for September 23th to 27th. The video will be shown in court during the hearings to follow.
The prosecution is expected to call some 360 witnesses, including Domnica Cemortan, a young Moldovan woman who was in Schettino's company at the time of impact, and coast guard official Gregorio De Falco, whose angry phone call to Schettino that night went viral after being leaked.
Schettino's lawyers have called 100 witnesses and plan to probe management at ship owner Costa Crociere, materials used to build the ship, and a malfunction of emergency doors and back-up generators.
On Thursday, they requested a fresh technical survey aboard the capsized liner, which is still lying on its side off Giglio island. The court said it would rule on the request later in the year, but ruled out sending experts aboard the ship before it is refloated and made safe.