Arsenal does have the opportunity to take first place from Man City, assuming the match between Man City vs Liverpool ends in a draw. But, Brentford is an opponent that is not easy to beat, moreover, in this match, Brentford will be playing at home. For this reason, Arsenal must play with all their might because once they are careless, Brentford could become their nightmare.
Apart from Arsenal, Liverpool also has a chance to take first place from Man City but this chance is not that big considering that the opponent they will face is Man City who is playing as the host. What is clear is that this match will be a tough battle for both of them.
Yes you are right if Manchester City and Liverpool draws the match and Arsenal wins there match they automatically become the premier League first team so there wish now is for the the both teams to draw because Manchester City is leading by 28 points on the group while Liverpool is leading with 27 and Arsenal with 27 points so if Manchester City and Liverpool draws they will have only one points added to the both teams and if Arsenal win they will have 30 points beating the Manchester City and Liverpool.
But however Manchester City and Liverpool are both so much in need of wining so is almost obvious that they will not play draw on that match because there growths on this premier league depends on that match.