Chester and Ellesmere Port's Labour MPs are both under investigation by parliamentary standards.
The allegations stem from before Christmas.
Mr Matheson, who holds the City of Chester seat, said he had provided a 'robust defence' to the Parliamentary Commissioner for Standards office.
He said: "I'm not allowed to comment on the investigation until the Commissioner clears me."
Mr Madders, who represents Ellesmere Port and Neston, has also denied the claims.
He said: “I am complying with the investigation and disputing the allegation. I am not able to comment any further at this time.”
Both Mr Matheson and Mr Madders have held their posts since the 2015 General Election.
The MPs' code of conduct states: "MPs are required to register within 28 days any interest which someone might reasonably consider to influence their actions or words as an MP."