It had been reported at the start of the season that PSG could part company with Blanc should they miss out on winning the Champions League.
However, Blanc dismissed such claims and, after witnessing his side beat Lyon 3-0 to reach the Coupe de France quarter-finals on Wednesday, he told France 3: "If this must be done in the coming days, it will be by the end of week."
Pressed on the issue, Blanc said he could sign the contract by "[Thursday] morning".
PSG face Lille in Ligue 1 on Saturday before facing Chelsea in the first leg of their Champions League round of 16 tie three days later.
READ MORE | REPORT: PSG 3-0 Lyon
Asked about his side's busy schedule, Blanc said: "If you speak to me about the calendar, I'm best avoided. Victory softens things.
"For the return match in the Champions League, we know the solution, but I have a team of players who want to win everything and I'm a coach who wants to win everything. There are no solutions, so we make do.
"We struggled to get into the match [on Wednesday], Lyon made us run, defend. In the second half we were much better. The players need these difficult matches to be good next week.
"The physical work in January is starting to bear fruit. There are no casualties. This is a very good thing."