The Uruguayan forward scored his second hat-trick of the campaign away to Wigan on Saturday, taking his league tally to 21 so far in 2012-13.
In doing so, Suarez became only the third Liverpool player to score over 20 goals in a Premier League campaign and his team-mate reckons that the ex-Ajax man has plenty more left in him.
|8/11||Luis Suarez is 8/11 with BetVictor to be the Premier League's top goalscorer
"He's scoring all different types of goals and, if you have a striker like that, you've always got a chance of winning games. He must have a big chance for the player of the year awards."
Suarez unsurprisingly grabbed the headlines after Liverpool's 4-0 win away at Wigan, but Downing was also keen to stress the importance of Pepe Reina to the Reds' victory.
"As we won comfortably in the end, some people won't see how important Pepe was against Wigan but as players we appreciate it," he added.
"If a keeper makes a mistake generally it ends up in the back of the net. It's a tough position to play.
"That save at 2-0 was really important. At 2-1 it would have been a different game. But Pepe kept it out and we pushed on, got the third goal and then it was easy for us. He's a top-class keeper."