Grice is to take over from Oliver Whitehead in August, but must first be voted back on to the board as an executive director at next week's annual meeting.
The National Association of Pension Funds has asked its members not to endorse Grice on the grounds that his contract put him on a two-year notice period, which is longer than is generally regarded as best practice.
The NAPF, whose members control about 20% of the £650bn in the hands of Britain's pension fund investors, said that Grice should not have a contract for more than a year. A spokesperson said: "The two-year contract is not in line with best practice. We recommend rolling contracts [of one year or less] to encourage performance and accountability."
The association has advised shareholders to abstain on a vote on the firms' executives' remuneration report. Again, its concern is over the two-year notice period enjoyed by Grice, and fellow board member Jeffrey Hume.
Alfred McAlpine was unavailable for comment.
The NAPF has made similar recommendations over the line its members should take at support services group Laing, contractor Balfour Beatty and developer Slough Estates, which all held annual meetings this week.
The NAPF was critical of Laing's decision to stand Baroness Noakes for election as a non-executive director because the NAPF does not consider her to be independent of Laing. (She has been a partner at KPMG, Laing's auditor, in the past three years.) The NAPF recommended members to abstain in that vote.
The NAPF is critical of Balfour Beatty over its use of two-year notice periods. It called for members to abstain over the remuneration report and the election of a director, Peter Zitkin.
Slough Estates was criticised over the lack of independence of a non-executive director.