MSP Michelle Ballantyne hopes to garner the required support of 100 party members to qualify for the contest to succeed Ruth Davidson as Scottish Conservative leader.
Davidson resigned in August 2019 amid changes to her personal circumstances and "conflict" over Brexit. Interim leader Jackson Carlaw was the first candidate to enter the leadership race.
Carlaw said upon declaring that he would "take the fight to Nicola Sturgeon and the SNP" in Scotland.
He tweeted: “We must take the fight to Nicola Sturgeon and the SNP, broadening our platform and diversifying our party. I'm ready for the fight."
A number of MPs and MSPs are already behind Carlaw, including former leadership rival Murdo Fraser and MSP frontbenchers Liam Kerr and Rachael Hamilton.
However, Ballantyne says that she will seek out support from the wider party membership in an effort to force a race for the leadership rather than a "coronation".
Ballantyne, who is also the party’s social security spokeswoman said: "I don't know yet about the MSPs and the MPs. But what I do know is that it's the grassroots, it's the membership that have been coming out in support for me so far and they're the people that I'm talking to.
"They're the people that really matter actually because we work for them."
She added: "I'm a democrat and I don't believe coronations are the right approach."
Nominations for the party leadership close on 17 January. Should Ballantyne or any other candidate win the required backing to force a contest, the result of the vote will be announced on February 14.
The winner will lead the Conservative Party in Scotland into the next Scottish Parliament elections in 2021.