The meeting comes ahead of an EU summit during which 27 member states, all but Britain, will adopt a protocol for negotiating London's divorce from the bloc.
Barnier, who will lead those negotiations, will meet Polish Prime Minister Beata Szydło and with Szymański, who is the government's negotiations proxy.
According to Szymański, Brexit could impact trade relations which hitherto have been “exceptionally easy and straightforward”, and saw a growth in sales volumes of goods and services.
“This could change substantially and that is why … representatives of the trade world should have as close contact with [the Brexit] process as possible,” Szymański said.
He added that the meeting with Barnier would be an opportunity for a “direct exchange of opinions, concerns, worries, and demands with the chief negotiator”.
Szymański also said that the 27 member states have a strong understanding of how Brexit negotiations should proceed.
“We all understand that EU unity … is the key issue in terms of the success of the negotiations”.
For Poland, the best result will come from maintaining current UK-EU relations, Szymański said.
“We want the exit process to be mild, orderly and not create too many doubts or concerns for citizens or the economy,” he said.
Another major concern for Poland is to guarantee the rights of Poles living in the UK.
“This is cause for a lot of political strain on the British Isles, so this will require a lot of imagination and work,” Szymański said.
Szymański added that the EU's budget concerns “need to be discussed so that we define the rules upon which we can part so that neither party feels wronged”.
Britain voted to leave the EU in June 2016. UK Prime Minister Theresa May triggered article 50 of the Lisbon Treaty in March, formally informing the bloc of the country's intention to leave.
The process is expected to end on 29 March, 2019. (vb/rg)