Fellow MSPs, Ken Macintosh and Charlie Gordon, may also stand, if they can secure sufficient nominations.
Mr Gray said on Monday he could offer his party "a new voice and a fresh start" as leader.
"Labour must re-establish trust with voters across Scotland by focussing on what matters to them, by working together as a party - across all levels - and by proving ourselves in holding the SNP administration to account more effectively," he said.
The new leadership team will be unveiled on 13 September and MSPs have until 1 August to secure the support of five colleagues to go forward to the next stage.
Among those eligible to vote will be the party's MSPs, MPs, party members and affiliates such as unions.
Mr Kerr, the former health minister, told BBC Radio's Good Morning Scotland programme on Monday that the party needed to concentrate on social justice and remind voters of the difference the Labour Party could make to their lives.
But he would not be drawn on whether he would support the SNP's plan for a referendum on independence in 2010, claiming First Minister Alex Salmond had not made clear what his proposals were.
Mr Kerr said: "This is not a play thing, this is about taking Scotland out of the UK and making it a separate country and I am not going to sign a blank cheque for Mr Salmond, for his chip on his shoulder about his attitude towards our colleagues in the rest of the country."
Ms Jamieson, the former justice minister, is expected to announce on Tuesday she will be standing in the contest, with Mr Kerr formally joining her later in the week.
Margaret Curran had previously been tipped to enter the race but this is thought to be less likely following her defeat as the Labour candidate to the SNP in the Glasgow East Westminster by-election.
BBC Scotland political editor Brian Taylor said it was not yet clear whether other candidates would come forward, adding: "Ken Macintosh may struggle to get sufficient nominations from MSPs.
"Charlie Gordon wants to stand but may be damaged by his role in soliciting the illegal campaign donation which finished Ms Alexander."
Mr Gordon resigned earlier this year as transport spokesman after admitting to making mistakes over a donation to Ms Alexander's leadership campaign.
The ensuing row over the donation led to Ms Alexander resigning as party leader after the Scottish Parliament's standards committee recommended MSPs vote to ban her from parliament for one day after she failed to declare donations on her MSP register of interests.
But Mr Gordon, the MSP for Glasgow Cathcart, told the Sunday Herald he wanted to put the affair behind him and "renew our leadership and renew our party".
Ms Jamieson will remain as acting Scottish leader until a successor to Ms Alexander is found.
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