"I've read through the speech and I've not seen the word impeachment," Gidley told reporters at the White House. "As he likes to say, we'll see what happens. But I haven't seen it."
Gidley said Trump is "intimately involved" in crafting the speech, which will begin around 9 p.m. on Tuesday (0200 GMT).
The president is expected to address economy, work family issues, health care costs, immigration, and national security, according to a senior administration official, Xinhua news agency reported.
Several Democratic lawmakers plan to boycott the speech.
Trump will not be the first US president to deliver a State of the Union address in the middle of a Senate impeachment trial.
President Bill Clinton, who faced a similar situation in 1999, delivered his State of the Union address on the very day his legal team began presenting his impeachment defense to senators.
After a months-long proceeding, final votes on articles of impeachment against Trump will be held Wednesday afternoon in the Republican-controlled Senate amid wide expectations that Trump will be acquitted.
Gidley said on Tuesday that there may be "an announcement or a statement or two" after the votes.
The House, controlled by Democrats, impeached Trump in December last year for abuse of power and obstruction of Congress, charges that the White House has refuted.
A whistleblower raised concern in an anonymous complaint last summer about the White House's interactions with Ukraine, triggering a Democrat-led impeachment inquiry against Trump.
The US president was alleged to have pressed his Ukrainian counterpart, Volodymyr Zelensky, into launching investigations that could politically benefit him. Furthermore, the White House allegedly tried to cover it up.
According to the US Constitution, the House shall have the "sole Power of Impeachment," while the Senate shall have the "sole Power to try all Impeachments."
Conviction can only happen in the Senate and requires at least two-thirds of its members, or 67 senators, to vote in favor of at least one article of impeachment after a trial. Currently, the Senate has 53 Republicans, 45 Democrats, and two independents who caucus with Democrats.
No sitting US president has ever been removed from office through impeachment.
( With inputs from IANS )