Feinstein, who has served California in the Senate since 1992, will be 85 on Election Day next November.
Feinstein said that she hopes to end gun violence, fix climate change, and improve access to healthcare.
"There's not a gang member in Chicago, who's going 'hey I'm going to get you, but first I have to go through Dianne Feinstein's background checks.' It's nonsense", he said.
On Sunday, Feinstein hinted in a national television interview that she was likely to run again, telling NBC's "Meet the Press" that she was close to a formal decision.
She would be running for her fifth full term.
The powerful lobby last week surprised many gun control advocates by embracing possible restrictions on the bump stock devices in the wake of the shootings that killed more than 50 people and injured 500, prompting bipartisan support in Congress for regulating or banning bump stocks. The devices were found on several of the weapons in the assailant's Las Vegas hotel room. Bernie Sanders (I., Vt.) with leadership from his 2016 presidential campaign, has vowed to back a primary challenger to oppose Feinstein. Congressional Republicans and President Trump have, however, called for a review of federal policy that now permits bump stocks.
Still, Feinstein is expected to have the support of most establishment Democrats already in office, and she already has the endorsement of her fellow California Democrat in the Senate. Adam B. Schiff, Eric Swalwell and Brad Sherman, were said to be preparing for a Senate campaign if Feinstein opted to retire.
The mere implication that Trump could be a "good president" drew the ire of state Senate president Kevin de León, whose recent two-day trip to Washington was seen as laying the groundwork for a potential Senate run.
Feinstein also has continuously expressed reservations about the so-called single-payer health care plan championed by many progressives, including Vermont Independent Sen.