Mrs Merkel spoke to the media at the end of the first day of a summit of EU heads of state in Brussels.
It came on the day Prime Minister Boris Johnson had set as a potential cut-off point for the acrimonious negotiations.
Mrs Merkel, the veteran diplomat, admitted the two sides had their own “red lines” but said the EU should be willing to compromise if the UK does the same.
She reiterated the protection of the single market and continued peace in Ireland were of vital importance to the bloc.
“We have requested the UK in the sense of an agreement to be willing for further compromise, this includes of course compromises from our side,” Mrs Merkel said.
For us it is important that Ireland can continue to live in peace, to safeguard the single market
“Each side has its own red lines. For us it is important that Ireland can continue to live in peace, to safeguard the single market.
“We also acknowledge that the UK would like to have a certain amount of independence since they are not an EU member.”
Britain has already left the EU, but Brussels and London need to agree on what their future relationship will be once a transition period ends on January 1.