David Cumming, head of equities at Standard Life Investments (SLI), said Mr Bolland would come under a "lot of pressure" if the M&S autumn fashion range was not popular.
The high street giant has been struggling with its non-food sales, with the most recent figures showing a like-for-like slump of 3.8%.
In a bid to improve that, Mr Bolland hired former Debenhams, Aquascutum and Jaegar boss Belinda Earl as style director in autumn last year, while Kate Bostock, head of general merchandise, left the company to be replaced by long serving executive food director John Dixon.
However, Edinburgh based Mr Cumming believes M&S has been slow to address its weaknesses and suggested the company. which has 67 stores in Scotland, could be vulnerable to a takeover.
He said: "[Mr Bolland] has to get his autumn range right, that's when the management changes that he's made, albeit late, will have an impact and I think the market will wait to see how that range, which doesn't really come through until six to nine months, how that's going to work. "
SLI, which holds a 1.7% stake in M&S worth around £100 million, is a powerful voice in the corporate sector and played a lead role in the so called shareholder spring of last year, which saw a number of companies successfully challenged on executive remuneration.
Mr Cumming said he believed Mr Bolland would hang on to his job in the "short term".
He added: "Marks and Spencer has made some progress in sort of secondary areas like logistics, etcetera, but the key issue is the performance of general merchandise, particularly clothing, and it's probably fair to say we're not comfortable with the progress here.
"They have made management changes but they have been a bit late."
Kate Calvert, retail analyst at Seymour Pierce, said her company shared Mr Cumming's view that the autumn season would be crucial but added it would be difficult to measure the success of those ranges until Christmas.
M&S has been in the spotlight since its downbeat festive trading figures – general merchandise sales down 3.8% with food rising at a lower than expected 0.3% – were leaked last week.
It has been seen as one of the retail losers in the crucial festive trading season while rivals such as John Lewis and Next have performed strongly. Mr Bolland – who has been in the chief executive since May 2010 after taking over from Sir Stuart Rose – said at the time of the results he was confident he would still be at the company to announce the Christmas 2013 trading figures.
Prior to joining M&S, the Dutch born businessman had turned around supermarket chain Morrisons following on from a successful career with brewer Heineken.
In November M&S reported a 3.3% dip in first half profits to £297m and signalled the benefits of the management reshuffle would become apparent in the summer.
When asked about SLI's stance on Mr Bolland, M&S said it did not comment on speculation.
Shares in the company ended the day down 5.3p at 367.2p.