The Bhoys have won 12 matches and drawn three from 15 thus far and Dutch centre-back van Dijk is looking at getting through to the end of the campaign without tasting defeat.
"Of course it is something everyone dreams of and we are going to try our best to do it," he told the Daily Record.
"We have the quality to do it and we have to stay focused. I think it is possible.
"We know what we are capable of and we saw it in the two games - against Hearts and then Motherwell - before we played Barcelona (and lost 6-1 in the Champions League). Hopefully, we can continue to play like that. We are now 15 games unbeaten, so we hope we can make this run last all season.
"We should be striving for it because with the quality we have in the team it is achievable.
"But we have to work hard and never take anything for granted like we never underestimate anyone now."
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