A Cabinet reshuffle is likely to take place once a new Taoiseach is appointed in the coming weeks
Denis Naughten says it would not make sense to change all of the Cabinet positions in a reshuffle.
The Communications Minister - who is an independent member of Cabinet - hopes to keep his current brief regardless of who wins the Fine Gael leadership.
The party says the turnout is 53% so far, with more constituencies voting this evening.
A majority of parliamentary party members - who have the largest share of the leadership vote - have come out in favour of Leo Varadkar.
Simon Coveney, in contrast, will have to pick up the votes of a vast majority of party members and Councillors in order to secure the leadership.
Minister Naughten - who heads the Communications, Climate Action & Environment Department - says he thinks he will retain his current portfolio, regardless of who wins.
He explained: "I've a very detailed programme of work in front of me. As you know, it's a new Government department - it was only established last July. It's taken a bit of time to bed that down.
"We've very complex negotiations going on at present at European level, in relation to reaching our 2030 [emissions] targets - and I don't think it would make sense to change that."
Results of the leadership election will be announced on Friday, after parliamentary party members vote.
Enda Kenny, who stepped down as Fine Gael leader earlier this month, will remain as Taoiseach until the Dáil votes to approve his successor.
Finance Minister Michael Noonan has already indicated he does not wish to be considered for a position in the new leader's Cabinet.