The prolific South African striker will be fit to face Moroka Swallows on Tuesday
Baxter was named Coach of the Quarter in the Absa Premiership on Monday, while Parker picked up the Player of the Quarter prize.
The Bafana Bafana striker says the influence of Baxter is what has helped him find his top form this season, after struggling last year under Vladimir Vermezovic.
"I speak almost every day with Stuart Baxter; he’s a top coach who has coached in Europe and worked for national associations,” Parker says.
“He told me during pre-season which areas I needed to work on and this can be difficult as you have to manage the player's intelligence.
“Things have worked out and the coach has brought the best out of everyone in the team.”
Parker is likely to be fit for the Absa Premiership clash against Moroka Swallows on Wednesday after limping out of Bafana’s 1-0 loss to Zambia last week.
He has played through the pain barrier for much of this season with the sore ankle, and is looking forward to the Soweto Derby with The Birds.
"It is a massive game. There is lot of history between the two clubs and there will be pride at stake. We need to continue where we left off against SuperSport United. We also go to this game knowing that past results do not count.
"Swallows are one of the toughest sides in the Premiership and we need not be fooled by their position in the log. We need to stick to our game plan.”