The Bank of England's Inflation Report in November showed that policymakers expect the jobless rate to rise to 5.4pc by the end of the year.
Saunders cited several factors that had contributed to the recent weakness in pay growth beyond low levels of inflation, including a rise in "less secure forms of work" and relatively high levels of under-employment, such as those in part-time roles would prefer to work in a full-time job.
These trends could become more common if economic growth slows rather than a rise in unemployment.
A rise in inward migration had also put downward pressure on pay growth, particularly in the context of low jobless rates, Saunders said, in areas such as London and the South East.
Increasing numbers of people going to university was also likely to boost employment and keep the jobless rate down, he said, while rising life expectancy and improved health would keep more people in work for longer.
Brexit uncertainty
Saunders said the outlook for the jobs market remained uncertain following the vote to leave the European Union last June.
He said the fall in the value of the pound following the vote and the expected increase in inflation could push up pay demands, which would gain traction if the Government restricts immigration and fewer workers decide to look for work in the UK from overseas.
By contrast, Brexit-related uncertainties could also "reinforce other factors dampening pay", as more people are forced to look for work or more hours as "higher inflation erodes household spending power".
While a lower unemployment rate was unlikely to prompt Bank policymakers to push up interest rates, the Bank would monitor developments closely and stood ready to act.
"If pay and other labour market guides give clear warning signs in coming months... this would have obvious implications for monetary policy, unless downside risks to economic growth rise significantly," he said.
Separate Bank of England data on Friday showed credit scoring on unsecured lending products such as personal loans "were reported to have loosened" in the final quarter of the year.
"Given mounting attention on the current strength of unsecured consumer borrowing, the Bank of England may well be perturbed to see that there was a loosening of credit standards for unsecured lending other than credit cards," said Howard Archer, an economist at IHS Global Insight.
Bank policymakers stressed this week that, while rapid growth in unsecured credit warranted close monitoring, total credit growth, including mortgages and the share of households using a large share of their income to service debts remained well below pre-crisis levels.