Wages are expected to rise and the unemployment rate remain at 4.9% when official figures are published on Wednesday.
Economists are pencilling in the jobless rate to stay the same as the three months to May when unemployment fell by 54,000 to 1.65 million.
Average earnings data is also predicted to pick up by 0.1% to 2.4% in the three months to June, according to consensus figures.
But these figures are likely to be eclipsed by claimant count data for July, which will give an indication as to how Britain's vote to leave the European Union is impacting employment.
Samuel Tombs, chief UK economic at Pantheon Macroeconomics, said: "June data will be overshadowed by claimant count and vacancy data for July, which will indicate how the economy has coped since the referendum.
"Meanwhile, wage growth likely was boosted by a favourable base effect in June.
"So, we expect the headline, three-month average rate of year-over-year growth in average weekly wages to pick up to 2.5% in June."
The update comes after the employment rate reached a record high of 74.4%, with 31.7 million people in work in the three months to May - 176,000 more than the quarter before.
The claimant count, including those on Jobseeker's Allowance, increased by 400 in June to 759,100, the fourth consecutive monthly rise.
London's top flight index hit a 14-month high on Monday, as investors expect this week's string of economic reports to give further insight into how the Brexit vote has hit UK economic growth.
Some investors believe the reports could spur the Bank of England into offering more support to the UK economy after cutting interest rates to 0.25% at the beginning of the month.
The unemployment announcement comes hot on the heels of Tuesday's Inflation update when the Consumer Price Index (CPI) rose to a higher-than-expected 0.6% in July.
CPI was up from 0.5% in June, according to the Office for National Statistics (ONS), with economists expecting the figure to be unchanged.
But while there was no sign of the plunge in the value of the pound having an impact on CPI, the ONS said the Producer Prices Index (PPI) showed sterling's slump had pushed up the cost of imports for British manufacturers.
Input prices rose 4.3% in the year to July, compared with a drop of 0.5% in the year to June, as the PPI was partly impacted by the fall in the value of the pound following the Brexit vote, which drove up the cost of imported metals and chemicals.