Griffiths took his tally for the season to 30 during Celtic’s 2-0 victory over Ross County on Saturday and still has 12 Ladbrokes Premiership games plus the William Hill Scottish Cup to work towards his next target.
“It would be great for him to do it and I believe that he can do it,” Brown said.
“It’s unbelievable the way he keeps going, he is so positive. Whether he misses one or two chances he will still go.
“It showed as well he has that other part to his game, against Ross County in the semi-final he was one on one with the goalie and he squares it for Gary Mackay-Steven to score.
“He is learning as well, it’s not always about him. He is bringing other people into the game and his link-up play has been a lot better.”
Griffiths has netted 57 goals in 92 matches in all competitions for Celtic since joining from Wolves in January 2014.
“Finishing-wise he is probably the best I have played with,” said Brown, who was speaking at the announcement that the Homeless World Cup will be staged in Glasgow this year.
“Everyone knew that he could score goals and play the way he can. He just needed to be given the stage to show he can do it.
“The way he has been in training and games has been exceptional. He gets that ball on his left foot, 20-30 yards from goal, and I fancy him to score wherever he is.
“It gives you that belief, once we go up the park there is always the wee man in the box scoring headers, overhead kicks, whatever he is scoring. He is there, he is a threat and is always on the defender’s mind as well.
“It’s great to have someone scoring 30-40 goals a season for you. It’s very hard to find these days and we have got one and he has just signed a new deal as well, so that’s great for us.
“Hopefully he can be pushing on in the Scotland squad as well because the wee man has come on leaps and bounds this season. I think he is loving life at Celtic and that shows on the park, how much he is enjoying his football.”
One Celtic striker who is not having nearly as much fun is Nadir Ciftci, whose loan spell with Eskisehirspor went from bad to worse on Sunday.
After being substituted 34 minutes into his debut the previous weekend, the former Dundee United striker was sent off after coming off the bench in a 3-2 win over Antalyaspor. Ciftci was shown a second yellow card in the 83rd minute following a high challenge on the goalkeeper.
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