The Saints responded to the disappointment of an early Europa League exit and the loss of striker Charlie Austin to a shoulder injury by beating Middlesbrough 1-0 at St Mary's Stadium on Sunday.
Reports suggested Van Dijk, now with the same representatives as Everton manager Ronald Koeman, could be a target when the transfer window opens in January.
Puel, though, dismissed any suggestion players were likely to be on the market as he remained focused on the job in hand of getting a result at Stoke on Wednesday night.
"It's not true
After the other thing is just speculation," Puel said when asked about a reported Â£25million buyout clause in Van Dijk's contract
"If he (Van Dijk) wants to change agent, it is not a problem for me
"After this no comment about speculation, just to say that Virgil is an important player for the team, for Southampton, of course.
"For me it is not a possibility to see him (move) away.
"It's important to consider this in this moment and to not speak further about this."
Saints head to Stoke in 10th place for the start of a run of games against sides around them in the table which sees a trip to south-coast rivals Bournemouth this weekend ahead of an FA Cup third-round tie at Norwich and then an EFL Cup semi-final with Liverpool
Puel said at a press conference: "To win the last game (against Boro) to come back after a big disappointment in a European game shows the strong character of my team
"To continue this work and to stay now in the first part of the table is very important from us and I think we will see this."
The Saints boss expects Stoke to offer a response of their own following a 3-1 defeat at title-chasing Arsenal.
"It will be a strong game against I think a very good team with great players," the French coach said
"They have great offensive players - with much potential - playing for them like (Xherdan) Shaqiri, (Joe) Allen, (Jon) Walters or (Wilfried) Bony and (Marko) Arnautovic - it is impressive.
"However, it is important to stay with good concentration about our own play and possibilities.
"We finished with a good second-half and a very good result in our last game and now it's important to find a good regularity for the next game and to take all the points if we want to do something for the second half of the season."
Source : PA