Turkey's centre-right government has said it will change article 301, but critics say that this has not materalised for fear of a nationalist backlash.
Breaking the law can mean a sentence of up to four years in jail.
Change of wording
Sahin refused to comment on the nature of the changes to the law before they were discussed at a cabinet meeting on Monday.
However, media reports have said that the term "insulting Turkishness" may change to "insulting the Turkish nation" or "insulting the Turkish people".
Sahin suggested that the justice ministry would have to give permission before proceedings could start under the article.
This would prevent nationalist prosecutors from exploiting the law.
Block to accession
Talks between Turkey and the EU have stalled due to human-rights disputes and Turkey's conflict in Cyprus.
Olli Rehn, the EU's enlargement commissioner, has advised that negotiations with Turkey should not progress until article 301 is changed.
Dozens of journalists and writers, including Orhan Pamuk, the Nobel literature laureate, have been prosecuted and convicted under the law, but none have been jailed.
Typically it has been used against those saying that the Ottoman Empire's massacres of Armenians in World War I were genocide.