The hip-hop star shocked the audience at the 2009 ceremony when he jumped on the stage in protest at Swift's win for Best Female Video - insisting the prize belonged to Beyonce for her hit, Single Ladies (Put A Ring On It).
West, who is reportedly planning to make his comeback with a performance at the 2010 awards show on 12 September, apologised to Swift following the embarrassing incident.
And now the hitmaker is furthering his bid to make amends by offering a track to the star.
In a series of posts on his Twitter.com page, he writes, "With the help of strong will, a lack of empathy, a little alcohol and extremely distasteful and bad timing I became George Bush overnight. Remember in Anchorman when Ron Burgundy cursed on air and the entire city turned on him? But this wasn't a joke. This was and is my real life.
"I wrote a song for Taylor Swift that's so beautiful and I want her to have it. If she won't take it then I'll perform it for her. I would never ever again in a million years do that. It is distasteful to cut people off as a general rule. What's the point of dressing tastefully if I'm going to act the complete opposite? When I woke up from the crazy nightmare I looked in the mirror and said, 'Grow up Kanye'. I'm sorry Taylor."