'Let us not waste time on this deal where there is no enthusiasm and it's very clear to me that it is not going to get support in the House of Commons. Let us look for a better deal', Foster told the BBC Radio 4 broadcaster.
The DUP leader stressed that a better deal should be good not just for Great Britain but for Northern Ireland as well.
'We, of course, are speaking to colleagues in the Conservative Party and indeed wider right across Westminster to try and find that better deal', Foster noted.
The party's chief concerns are linked to the backstop solution for Northern Ireland, which would see all of the United Kingdom remain in a customs union with the European Union. However, Northern Ireland would be subject to separate regulations as well, which could lead to more checks on some goods between the region and the rest of the United Kingdom.