If your question regards any family connection, then no. They don't share the same genes.
However, every few years, people are trying to find a new heir to the best player of all times, and name some young argentinean player, thus adding to the pressure on him.
In this case, Maradona himself mentioned once that Messi reminds him of himself. They're both short, lefties and can do whatever they want with the ball.
Messi is playing in a slightly different position, and is basing much on his velocity, which is something Maradona didn't have.
There were two Messi goals lately that really resembled two famous Maradona goals from the quarter finals against England in the 86' world cup in Mexico.
The first, against Getafe, in the first leg of the spanish cup semifinal, you can see here in a nice comparison between the two.
The second, last week, in a league match against Espanyol, was scored using his hand.
However, Messi still has a lot to prove to be worthy of this comparison. He still didn't win any title with the National team, and is now playing with some of the best players in the world around him (Maradona was the only player worth something in most of the teams he played).
