There is post-war testimony from two high-ranking officials (Walter Warlimont and Karl Jesko von Puttkamer) that Hitler had an interest in seizing Iceland but there are no record of concrete plans or anything that would indicate a serious intention by Nazi Germany to invade Iceland before the British did.

We do however have records that show that Hitler was displeased with the British occupation of Iceland and that he immediately tasked his commanders to draw up a plan and examine the feasibility of taking Iceland from the UK. The report/plan found that while an invasion could be successful, it would be too be costly to maintain supply lines to Iceland and not enough benefits in holding the island (no infrastructure for aircraft).

The expert on this period of Icelandic history is Thor Whitehead in case you want to study this issue further.