David Cameron is expected to be present despite German Chancellor Angela Merkel visiting parliament the same day.
According to BBC Cymru/Wales
the gathering follows the sacking of four shadow cabinet ministers by Welsh Tory leader Andrew RT Davies.
There are also tensions between him and the Secretary of State for Wales David Jones.
Mr Davies's chief of staff, Antony Pickles, was called to a meeting in Downing Street on Tuesday evening as No 10 tries to resolve the rows.
There is said to be puzzlement in Downing Street over the sackings and a desire to find out what happened and why.
Tuesday's meeting was said to be about finding a way through the tensions and to prepare for Thursday's gathering.
Wales Office Minister Stephen Crabb has cancelled an official visit to promote tourism so he can attend the meeting.
Last week, Mr Cameron said plans to hand restricted tax powers to Wales are the "starting point" for a debate.
UK ministers want to hold a referendum on allowing the Welsh government to vary income tax rates.
Each income tax band could only be moved at the same time and by the same amount - the so-called "lockstep".
A row over whether to back the lockstep or not led to Welsh Conservative leader Andrew RT Davies sacking four members of his shadow cabinet.
Mr Davies has criticised the lockstep while the four colleagues he sacked said they were supporting the policy of the UK coalition government.
So the four were sacked for supporting Cameron's Policy
It will be interesting to see what Cameron makes of former Shadow Minister who was sacked after defying her group leader in a vote over the devolution of income tax powers to Wales has made a formal complaint to the party about the behaviour towards her over the issue of a fellow Tory AM.
North Wales AM Antoinette Sandbach claims Darren Millar put unreasonable pressure on her to back the position taken by Andrew RT Davies.
So what what will the headmaster make of this will he back Andrew RT Davies his party leader in the Assembly or his Shadow Welsh Secretary.
Backing Mr Davies and indeed changing the Westminster proposals could be seen as listing and present the Welsh Tories with a victory.
Except there doesn't seem to be much support for Mr Davies amongst senior Welsh Conservatives outside the Assembly.
It seems that the Tories are digging themselves into a hole that they are going to find difficult to get out of.
Removing Andrew RT Davies would probably not be wise, But as long as there's a power struggle between the leader of the Tories in the Assembly and the Welsh Secretary (or Shadow) this will continue.
The same could be said of Labour but at least they are not conducting a civil war at the moment.