When asked in a Twitter Q&A if she would work with Taylor, Katy replied: "If she says sorry, sure!"
However, the 31-year-old star's family are less positive about the chance of a peace offering as Katy's father previously claimed her feud with Taylor "ain't over yet".
Mary said: "Katy released 'Rise'. It says, 'My feet have been put to the fire but I will rise.' That's what she's about right now."
Whilst Keith added: "You know it ain't over yet."
Katy and Taylor's spat was highlighted recently when the 'I Knew You Were Trouble' hitmaker's ex-boyfriend Calvin Harris slammed the singer in a rant.
In a series of tweets, he wrote: "Hurtful to me at this point that her and her team would go so far out of their way to try and make ME look bad at this stage though. I figure if you're happy in your new relationship you should focus on that instead of trying to tear your ex bf down for something to do
"I know you're off tour and you need someone new to try and bury like Katy ETC but I'm not that guy, sorry. I won't allow it. Please focus on the positive aspects of YOUR life because you've earned a great one. God bless everyone have a beautiful day (sic)".
Katy and Taylor have had an ongoing feud ever since the 26-year-old star claimed the 'Unconditionally' singer nicked three of her backing dancers from her 'RED' tour in 2012.