Rangers have lost two of their opening four Scottish Premiership games, including being beaten by Celtic in the Old Firm derby at Ibrox on Sunday.
A heavy defeat at PSV Eindhoven last week also meant that they failed to reach the group stage of the Champions League and will again play in the Europa League this season.
A section of the Rangers fans have already turned against Beale, who carried out an overhaul of the squad by bringing in nine new players in the recently-concluded summer transfer window.
However, former Celtic striker Hartson stressed that the talk of sacking Beale at Rangers is a bit premature at an early stage of the season.
He did admit that the Rangers boss is under pressure following a poor start to the season but indicated that he should be given more time.
The former striker said on the Go Radio Football Show: “[There is] talk of him getting the sack. I don’t agree with it.
“I think the problem you have got is that when you are losing games, then you are going to come under pressure.
“They have lost two of their opening four games and got thumped in Europe.
“He is going through a tough time at the minute but I think the talk of sacking Michael Beale is very premature.”
Beale will hope to fix some of the issues in his team over the course of the ongoing international break.
