The Saints players and staff will soon return to training ahead of their qualifying match for the Champions League, having qualified as Cymru Premier champions.
Even if TNS win or a lose in the first qualifying round, they will be handed the chance to move into the qualifiers for the Europa League or Europa Conference League.
Club chairman Mike Harris has reiterated his desire to qualify for the Conference League group stages and Harrison insisted that is what his side will be trying to do this year.
He said: “It is plain and simple, Mike (Harris) has made it clear, we want to put ourselves in a position to qualify for that elusive group stage.
“The Champions League is tough, Europa there is a glimmer but with the Conference League there is an opportunity.
“Look at Dundalk, they did it, Shamrock in Ireland did it.
“We have to try and emulate them as much as possible, and that is what we will be trying to do.”
The draw is yet to be made for the qualifiers that begin at the end of June.
Harrison believes if his side can win their first Champions League qualifier, then the statistics are on their side.
He added: “When I was here in my first spell there was no Conference League, it is a different format.
“That gives the lower team, not just TNS, an opportunity of a second and third bite of the cherry.
“The all important game is the first one, we know how important that is.
“Then when you get through that you are guaranteed an opportunity to get a play-off for the Conference League. That is the important one and we’ll be doing all we can to try and get through.
“Statistically, three of the four teams that make it through the first round have gone on to the Conference League, so that is our big focus.”