Wakely hit a superb 112 and Rob Keogh made an unbeaten 105 as Northants declared on 289 for seven.
That gave David Ripley’s men a 393-run advantage and 16 overs of the third day to try to take some Leicestershire wickets.
But the away side closed on 44 without loss, needing 350 runs on the final day to earn the win.
And Wakely knows Leicestershire are capable of getting the job done if Northants - and weather conditions - play into their hands.
“Rob (Keogh) came out with positive intent from the start and that made it easier,” Wakely said.
“We’ve been striving for hundreds from the middle order so we’ve ticked that one off, got a good partnership together and that was pretty pleasing.
“We’re now in a really good position in this game, we’d have liked a couple of wickets before the close, we bowled well but they batted well.
“Hopefully it’s cloudy tomorrow because Leicestershire have got some talented batsman that can win them this game.”