No, the Muslims are followers of the prophet Mohammed. Islam is the religion based on Mohammed’s teachings and Muslims are the members of that religion.
However, Abraham’s first son, Ishmael, was the grandfather of some of the Arabs. When Abraham sent Hagar and Ishmael from his home and expelled them to the wildness, God heard Hagar’s pray of grief. God responded with a blessing: “And as for Ishmael, I have heard thee (Hagar): Behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation.” (Genesis 17:20) Ishmael lived 137 years, and as promised was the father of 12 sons.
According to Genesis 25:13-18, Ishmael’s sons settled from Havilah to Shur. Geographically, Havilah had to reach the Sinai Peninsula, where most likely lay the wilderness of Shur. These verses show that Ishmaelites camped on the region extending from the Sinai Peninsula by north Arabia to Mesopotamia. It is an area still inhabited, today, by descendants of the Ishmael-Arabs.
After Abraham’s wife, Sarah, died, Abraham married Keturah (Genesis 25:1,2). Keturah had 6 sons whose descendants were the Midianites and Kenites. Those peoples founded the nations of Midian and Kedar. Today, these lands are in areas of Saudi Arabia and other Arab nations.