The Lords Commissioner for Standards has confirmed receiving a letter from Baroness Warsi, in which she asked him to investigate her expenses.
A spokesman for Paul Kernaghan said:
The Commissioner has received a letter from Baroness Warsi asking him to look into the allegations against her.
We have also had indications from a third party that they will write and complain, but we haven't received that yet.
The Commissioner has to do an initial assessment of the allegations and check whether it falls within his remit and see if it needs further investigation.
If it does he will launch a formal investigation, but we aren't at that stage yet.
It is understood that the third party mentioned is Labour MP John Mann, who said he would write to the Commissioner.
Asked whether he feels that Baroness Warsi should resign, chancellor George Osborne told ITV News:
"Baroness Warsi has written to the relevant person at the House of Lords and I think we can leave it at that."
He declined to answer further questions on the subject.
Baroness Warsi insists she takes the allegations over her expenses very seriously.
Arriving in the Malaysian capital Kuala Lumpur, she told ITV News that she would fully co-operate with any investigation.
However the Conservative Party co-chairman refused to say whether she would resign over the row.
Liberal Democrat backbencher Bob Russell has increased the pressure on Conservative Party co-chairman Baroness Warsi.
He thinks her expenses claim should not just be the subject of a parliamentary probe, but also a criminal investigation.
I think there's a prima facie case for this to be looked at by the police.
Tory MP Louise Mensch has come to the aid of Baroness Warsi, in a row over parliamentary expenses.
She told ITV's Daybreak that the co-chairman of the Conservative Party had done nothing wrong, by claiming for accommodation while staying at a friend's house.