The Canaries confirmed they had passed on evidence to Norfolk Constabulary which was supplied to them by supporters in the wake of Saturday's Barclays Premier League draw at Everton.
Press Association Sport understands Norwich have sent police screen-grabs of tweets that have since been deleted from Twitter accounts that no longer exist.
Manager Chris Hughton told a press conference on Monday it was "hugely disappointing" to learn of the alleged abuse of Bassong, who scored a stoppage-time equaliser in the 1-1 draw at Goodison Park.
He added of the tweets: "We have taken the appropriate action and passed them on to police."The alleged racist abuse of Bassong took place almost a year to the day that Norwich reported similar tweets directed at former Everton striker James Vaughan.
Bassong's goal at Goodison extended the Canaries' unbeaten run to seven matches in all competitions ahead of Wednesday's trip to Southampton, which is followed by games against Sunderland, Swansea, Aston Villa and Wigan.
Hughton's men will be confident of maintaining their good form, although the settled line-up could be disrupted by injuries to John Ruddy and Michael Turner.
Hughton confirmed Turner would be out for "a few weeks" with the shoulder injury that kept him out of the Everton game, which saw Ruddy substituted late on with a thigh problem.
If Ruddy fails to recover, Mark Bunn will make his first Premier League start for the club.
After an awful start to the season, Southampton have hauled themselves out of the drop zone with back-to-back wins.
Hughton said: "They have been playing well and come into it on the back of two great wins, so we know that it will be tough.
"We are also on a good run of results and need to maintain our recent high standards on Wednesday evening."
Wednesday's match also heralds the return of Mark Clattenburg to refereeing following the dismissal of allegations he racially abused Chelsea midfielder John Obi Mikel.
The 37-year-old was the fourth official in Tottenham's win over West Ham on Sunday but Wednesday will mark a month since he was last the man in the middle.
Hughton said: "I think he will get a good reception.
"I, for one, am certainly pleased he is back after all that happened."