Obviously, a decision like this would have to come with the support of those that currently have veto power. There's absolutely no reason whatsoever for them to be receptive to that, all it would be is willingly giving up influence. It's technically possible to abolish it, but realistically it's just not going to happen.
No, I do not think that it is possible for the UN Security Council to abolish the veto power. The veto power is strongly needed for the council to do its responsibilities and to hold up its power when it comes to national rights for all nations, and the ability to abolish is key for the UN Security Council.