"I am deeply flattered by the enthusiastic expressions of support I have received over the last 12 hours, and I am very seriously considering the race," Daniel M. Donovan Jr., district attorney for Richmond County, said in a statement Tuesday.
Donovan's announcement comes a day after Grimm reversed course and said Monday night that he would resign his seat Jan. 5, a day before the new Congress convenes, following his guilty plea last week to a single felony count of tax evasion.
Grimm, who easily won reelection in November, had vowed to hold his seat despite the 20-count federal indictment.
"This decision is made with a heavy heart," Grimm said in a statement announcing his resignation, "as I have enjoyed a very special relationship and closeness with my constituents, whom I care about deeply."
House Speaker John Boehner (R-Ohio), who met with Grimm on Monday a GOP source confirmed to The Hill, said Grimm "made the honorable decision" by stepping down.
"I know it was made with the best interests of his constituents and the institution in mind, and I appreciate his years of service in the House," Boehner said in a statement Tuesday.
Grimm faced bad publicity early this year, after he threatened to throw a local reporter off a Capitol balcony and break him in half in an incident that was caught on camera.
Donovan said he has "been asked by numerous elected officials, party leaders, supporters and the media" over the past week about potentially running in the district represented by Grimm since 2011.
"My response was that at that time there was no vacancy so any discussion of a run was premature," Donovan said, adding his phone "has been ringing off the hook" since news emerged Monday night that Grimm would resign.
"I will make an announcement after the due deliberation such an important decision deserves," Donovan said.
New York Gov. Andrew Cuomo (D) will declare a special election to replace Grimm following his resignation, and party leaders will caucus to choose their candidates to place on the ballot.
In addition to Donovan, other potential Republican candidates include Assemblywoman Nicole Malliotakis, who is reportedly "taking a serious look at the seat," and state Sen. Andrew Lanza, according to the New York Daily News.
Democrats have pounced on Grimm's resignation as an opportunity to win back the swing district. Even though the Staten Island-based district typically votes Democratic in presidential years, it has trended red in local and midterm elections.
“The people of Staten Island and Brooklyn were lied to throughout the last election by Michael Grimm and, sadly, Republicans let it happen despite his legal troubles," Democratic Congressional Campaign Committee Chairman Ben Ray Luján (D-N.M.) said in a statement Tuesday.
"Now voters will finally get the choice to get out from under the shadow of the scandals that have plagued Republicans holding this seat in recent years," Luján said, vowing Democrats "will have a candidate who will fight to grow the middle class and ensure the deck isn’t stacked in favor of the special interests and the wealthiest few.”
Among Democrats, former Rep. Mike McMahon told the New York Post he is considering a bid, while Assemblyman Michael Cusick was named as another potential candidate.