McHale, 26, has made three appearances for the Boro this season, scoring in a 4-2 defeat at home to Marske United.
The former Manchester City academy player most recently enjoyed two seasons with National League North side Telford where he made 34 appearances and scored six goals, before joining Darlington on loan for the remainder of the 2021/22 season.
Prior to his time at the Bucks, McHale had playing experience at Barnsley, Northwich Victoria, Salford, Southport, Oldham Athletic, Ashton United and FC United.
The attacking midfielder joined Radcliffe before the start of the 2022/23 season and featured in their 1-0 victory at home to Matlock Town.
McHale goes into Matlock Town's squad to face Guiseley tonight.
Photo credit: Mike Sheridan/Ultrapress
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