Islamic Apologetics would like us to believe so.
However, both “belief” systems are as chalk and cheese. Nothing is common betwixt them. Except rancor and rumor.
Islam holds GOD is absolutely “OTHER”. In Sufism there is “NO OTHER”. The “Core of Sufism” is NOT “To Strive for Nearness to God” but “ONENESS with GOD”. Quran postulates death for those who, like Jesus, proclaim “I and MY FATHER are ONE!” [St John 10.30] Sufis do.
Quranic Verse (50:16), of God being “closer to you than your jugular vein”, is often cited as “living” proof of Identical Teachings of Mohammedans and Sufis. Said Bulle Shah: “Wiped Off is Ink on Kalma!” [The 1st Confirmatory Verse of Quran/Mohammed being Allah’s Prophet].
Be it Rumi or Shamas Tabriz; by Strict Interpretation of Quran, Sufi’s “faith” is “Kufr”/Un-Truth. Such mystics, “Kafir.” Mansoor Al-Hallaj was cut to bits for proclaiming “An Al Haq” [I am The Truth] - as per Sufi’s SELF-REALIZATION of ULTIMATE REALITY, of ONENESS with “THAT” Which Is: God!
This is Apostasy in Mohammedan Belief.
Islam believes in a “man-like” anthropomorphic god. This is not The “Buddha” Experience of Sufis. Such “Duality” is annihilated - “overcome” - in DIVINE UNITY.
Much as humankind wishes for peace with Islam; it cannot come unless we all realize, as Sufis do, that “ALL IS ONE”. To “filter down” Sufism and “doctor” it to Islamic Belief does not cut it.
Sufism is not Islam.