Van Dijk joined the Saints from Celtic in the summer transfer window, and he has gone straight into Ronald Koeman's starting line-up.
Merson said that although the Dutch international struggled against Manchester United, he still expects big things from him in the future.
"Against Manchester United, I thought [Anthony] Martial gave him the run around, but it's going to take time," Merson said on Sky Sports' Soccer Saturday. "I think he'll get better and better, he looks decent.
"The other thing is that when he goes up for corners, he goes up there to score goals.
"He doesn't go to make up the numbers. I think he'll score goals and he'll get a lot better, there's no doubt about that."
Van Dijk made a habit of being a fairly frequent scorer for a defender at Celtic in the Scottish Premiership, and he netted 15 times in 114 games for the Scottish giants.
He has already shown his goalscoring threat at Southampton, too, when he nodded in a corner against Swansea City in one of the Saints' recent fixtures.
It has been Van Dijk's defensive ability which has impressed the most, though, as he has slotted into Southampton's backline with ease.
The 24-year-old was in brilliant form as the south coast club picked up a 3-1 win against Chelsea in their latest outing, and he appears to have adjusted to Premier League football very quickly.