MEP Seán Kelly has said he will "most likely reconsider" his possible candidacy in the presidential campaign "in light of Mairead [McGuinness'] unfortunate withdrawal".
It comes after former Fine Gael MEP Frances Fitzgerald ruled herself out of running for the party in the Presidential Election.
The former justice minister said her mind had not changed in the wake of Mairead McGuinness' withdrawal.
She said her decision remains as it was last year.
"I made the decision not to contest then, and I won't be seeking a nomination."
This afternoon Independent TD Michael Healy-Rae said he would back Fine Gael's Heather Humphreys "wholeheartedly" in the presidential election.
He said Ms Humphreys would be an "excellent candidate", after Ms McGuinness' shock withdrawal.
Mr Healy-Rae said he would be "100% in her favour" and called Ms Humphreys a "highly capable lady".
He said he believed Ms Humphreys would galvanise others outside her party and would appeal to a wider base than Fine Gael.
He said there are "people up and down the country, from all parties and none" that would support Ms Humphreys.
Watch: Healy-Rae says Humphreys would have 'broad appeal'
He said her "performance over the years", her policies, the "way she carried herself" and the "way she answered questions" would all work in her favour.
Ms Humphreys is seen as someone who would benefit from support from outside the party.
She retired from politics last year saying she wanted to spend time with her family, but it is understood the former Minister is considering her options.
The former Cavan-Monaghan TD has been contacted for comment.
Senior Fine Gael figures say they expect that another candidate will be nominated by the party to run in the election.
Ms McGuinness said she was stepping aside due to health concerns.
The Fine Gael Executive Council will meet in the next few days to discuss its plans.
There is a feeling, however, that the party will nominate another person to run.
One former minister said they believed Fine Gael should definitely nominate another candidate, while another said it was "likely, but not certain".
Names previously associated with the job also include Seán Kelly.
Independent TD and presidential hopeful Catherine Connolly has said the statement from Mairead McGuinness was shocking and wished her all the best.
Ms Connolly said she deliberately declared early and does not regret the decision, noting it allows for scrutiny.
Tánaiste Simon Harris said yesterday that there is a great sense of shock in Fine Gael following Ms McGuinness' decision to withdraw from the presidential race on health grounds.
In a statement released yesterday afternoon, Ms McGuinness said the decision was not taken lightly, and followed a stay in hospital last week.
Mr Harris said Ms McGuinness is a "great colleague" and a "great friend" and is somebody who has served her party and her country with distinction.
He said while Ms McGuinness had been working hard in preparation for the presidential election, her health has to come first.
"It's absolutely crystal clear that on the basis of health advice, she is making the right decision," Mr Harris said.
Ms McGuinness said she is taking the decision on medical advice, and it is the "right decision" for her and her family.
"My priority now is my health. Given that the election is in a short couple of months, I do not believe that I have the strength to give the campaign my all," she said in a statement yesterday.
'Great sense of shock in Fine Gael' on McGuinness withdrawal - Harris
Mr Harris said Fine Gael will convene its executive council in the days ahead and consider the next steps on any potential presidential candidate.
In a statement yesterday, Fine Gael's Director of Elections for the upcoming presidential election Martin Heydon confirmed the meeting will take place in the coming days.
Catherine Connolly also said that it was very early to be talking about her current favourable position.
But she said the feedback on the ground was excellent and that she will be on the campaign now every week going forward.
Fianna Fáil has yet to decide whether it will run a candidate while Sinn Féin is considering its options with a decision to be arrived at in a few weeks.
Yesterday, businessman Gareth Sheridan launched his campaign for the Áras, and said he is confident he can be proposed and seconded by six local authorities after having secured the support of Tipperary and Laois county councils.
Read more:
Fine Gael focus in coming days to shift to new candidate
Mairead McGuinness withdraws from presidential race
Presidential hopeful Gareth Sheridan says he has backing of two councils
