Martin Strel, 47, started swimming the river's 2,340 miles (3,765 kilometers) last month at its source at Lake Itasca, Minnesota.
He spent several hours Saturday off the banks of Dyer County and is expected today to reach Tomato, a boat landing near the Lauderdale-Tipton County line.
Strel, the father of two, already holds the record for the longest swim the 1,776-mile (2,857-kilometer) Danube River in Europe. He also is the world's longest nonstop swimmer 312 miles (502 kilometers) in 84 hours and 10 minutes.
Saturday marked his 44th day of spending between eight and 10 hours in the Mississippi. Strel began in Tiptonville, stopped for lunch at the Kent Ford boat ramp and ended the day at a takeout in Lauderdale County about 40 miles (65 kilometers) from where he started the day.
Heaving down a carbohydrate-heavy soup laden with pasta, vegetables and bread at the boat ramp, Strel said in broken English he is swimming the Mississippi "because 10 years ago United States recognized Slovenia as a nation. I want to be first man in history to swim the Mississippi.''
Strel started his swim July 4 and plans to finish Sept. 7, the 10-year anniversary of the United States' recognition of Slovenia as an independent country.
Others have swam large portions of the Mississippi, but no one has gone from the headwaters to the Gulf of Mexico, 80 miles (130 kilometers) south of New Orleans.
Strel is averaging more than 40 miles (65 kilometers) a day in the wide lower Mississippi, almost twice the speed he traveled in the river's upper reaches, where dams, locks, and even trees became obstacles.
Despite swimming about 10 hours a day, Strel said he does not feel soreness or pain until at night, when his shoulder gives him trouble.
The adventure has had its harrowing moments. On Wednesday, north of Cape Girardeau, Missouri, a lightening bolt struck the river about 6 feet (1.8 meters) from him. He left the water and waited for the storm to pass.
Strel is accompanied by a team of three kayaks, a canoe and a support boat that follow him in the water to make sure he is safe.
A recreational vehicle is also part of the support network, meeting Strel and his crew for lunch and dinner.