The North Shropshire MP said fears that working with members of the right-wing Northern Ireland unionist party could lead to a backtrack on issues such as gay rights and abortion are unfounded.
Mr Paterson said the two parties had much in common and there was no reason why talented politicians from Northern Ireland should not "rise to the top" of UK politics following the Belfast agreement, as Republicans such as Gerry Adams had done in Ireland.
His comments came as Scottish Conservative leader Ruth Davidson raised concerns over the DUP's stance on issues such as same-sex marriage, seeking assurances from Mrs May over gay rights as the Conservatives seek to enter into a partnership with 10 elected DUP MPs to bolster the 318 Tory MPs and create a majority in parliament.
But Mr Paterson said many issues such as same sex marriage and the law on abortion were devolved matters anyway so unlikely to be an issue for forming a UK government.
He said: "These issues are devolved and if they were sorted in the English parliament they would be free vote issues anyway. I really don't see them colouring talks."
He said in many cases the issues had already been debated and resolved in each nation so any backtrack was unlikely, adding: "You might get a debate I suppose on further reduction of abortion times as medical science advances."
The MP, a staunch supporter of Brexit, said the most pressing matter was the imminent negotiations with the EU.
"We are nine days away from the talks starting and I don't think it's actually a bad thing at all, considering one of the most contentious issues will be the Irish border, to have the DUP involved with people on the ground who quite rightly want to maintain a common travel area and maintain the easiest possible free movement of goods and services and people, which is exactly what we all want," he said.
"There is an immediate problem to get a government fixed with a workable majority so that we can begin to work on Brexit – this is coming down the track, the train is approaching and we have to get that resolved.
He said it was right for Theresa May to carry on as Prime Minister as "to have the chaos and uncertainty of a leadership contest would put the whole issue on hold".
He said Jeremy Corbyn had done very well but was still "a mile off on seats" even if he teamed up with every other opposition party in parliament.
"He couldn't get to 326 so it is quite right that the Prime Minister, who is very nearly there at 318, does sit down with a party with whom we do have many things in common, particularly resolving Brexit, and see if she can find a way forward," he said.