The hosts head into the match off the back of a 2-1 league win over Aberdeen, while the visitors suffered a 2-1 defeat to Dundee United in the Scottish Championship last time out.
Match preview
Under Philippe Clement's leadership, Rangers have experienced something of a resurgence, clinching the League Cup for the first time in over a decade and currently mounting a serious challenge for the Premiership title alongside Celtic.
The Gers are currently just three points behind their Glasgow rivals with a game in hand, and after their victory over Aberdeen at the weekend, Clement's side are now on a seven-match winning streak in all competitions.
The new manager's sole blemish since arriving at the Ibrox Stadium came in the New Year's derby against the Hoops and is the only defeat the team has conceded since a 2-1 loss to Aris Limassol in the Europa League on October 5.
In this competition, Rangers eased past Dumbarton 4-1 in the previous round and rattled in nine goals in their following four league games leading up to this match while only conceding two in that time.
It comes as no surprise to see the hosts set as the overwhelming favourites according to the bookmakers, as they have won each of their last seven matches against this opponent and outscored them 21-2 during that win streak.
Meanwhile, Ayr United saw their three-game unbeaten league run brought to a halt last weekend when Dundee United staged an excellent second-half comeback to clinch the points in a 2-1 win at Somerset Park after going 1-0 down in the opening two minutes of the match.
That result marked the Honest Men's 11th league defeat of the season and left them in sixth place after 23 matches in the Scottish Championship, 11 points behind the top three teams and having played a game more than all the sides above them.
Their uninspiring form this season led to the axing of now-former manager Lee Bullen last month, with Scott Brown being appointed as his successor, but while there have been positive signs since the arrival of the former Celtic and Scotland captain, this is a whole new level of difficulty for his side, especially given the run of form his opponents are on.
In addition, the visitor's away record does little to improve the outlook for their chances in this match, having only managed to win one of their last eight games on the road across all competitions in regulation time.
Rangers Scottish Cup form:
W
Rangers form (all competitions):
W
W
W
W
W
W
Ayr United Scottish Cup form:
W
Ayr United form (all competitions):
L
D
W
W
W
L
Team News
Rangers will be without the services of several players for this match, starting with Dujon Sterling, who is suspended for this one after being sent off in the closing stages of the match against Aberdeen last week.
Kieran Dowell (knock), Kemar Roofe (knock), Danilo Pereira (knee) and Abdallah Sima (thigh) are ruled out of this match due to injury, while Leon Balogun is flagged as a doubt.
George Stanger will take no part in this weekend's trip to the Ibrox Stadium for Ayr after he was sent off in stoppage time in the side's 2-1 defeat against Dundee United last time out.
Frankie Musonda has not played since returning from the Africa Cup of Nations with Zambia but could make the starting lineup here in place of the suspended Stanger after featuring on the bench last weekend.
Rangers possible starting lineup:
McCrorie; Tavernier, Goldson, Souttar, Yilmaz; Cantwell, Lundstram, Raskin; McCausland, Dessers, Matondo
Ayr United possible starting lineup:
Albinson; McAllister, Musonda, McGinty, Reading; Syla, Dempsey, Murphy, Mcgeady; Dowds, Willoughby
We say: Rangers 3-0 Ayr United
It is difficult to make much of a case for Ayr United in this match as they head to take on arguably the most in-form side in the top flight at the moment. Therefore, we will keep it short and sweet - we fancy Rangers to cruise to an easy victory in this one.