The financial industry and many Republicans oppose her nomination because of concern should would be too harsh on banks.
She is the leading candidate to head the Consumer Financial Protection Bureau that will create and enforce new regulations on financial products such as credit cards.
An announcement from the White House could come as early as this week.
Durbin said he has discussed a possible appointment with the White House and said he didn't think naming her to the position would put the new agency in jeopardy.
"Frankly I don't know what the White House will propose but I don't know how you can undermine an agency with the concept she created," Durbin said. "She authored it and to put her in charge of it is the appropriate thing."