Rightmove said the number of homes on the market with two bedrooms or fewer - properties often favoured by first-time buyers - is up by 1.9% compared with a year ago.
The start of last year saw a rush of buy-to-let investors snapping up homes to beat a stamp duty hike for second home buyers which came into force on April 1 2016. This year, first-time buyers may find they have less competition from landlords.
But people taking their first step on the property ladder may have to stump up more cash than they would have done a year ago.
Rightmove, whose figures cover England and Wales, said the average asking price for a typical first-time buyer home in January was £188,612 - over £4,700 more than the typical asking price of £183,900 in January 2016.
Across England and Wales generally, the average price tag on homes of all sizes increased by 0.4% month-on-month in January, pushing it back over the £300,000 mark. In January, the average asking price was £300,245, up from £299,159 in December.
Rightmove said early indicators of buyer demand are generally "robust", with its website traffic up by 5% since Boxing Day compared with a year earlier.
Miles Shipside, director of Rightmove, said: "Those planning to buy their first home in 2017 have more choice of properties and less competition from other buyers than their counterparts a year ago...
"Some sellers of first-time-buyer properties may be being over-optimistic with their pricing, giving an opportunity for budget-strapped first-time buyers to negotiate, especially if they act now while there's still more choice available."
Looking across the country, East Anglia has seen the biggest jump in asking prices over the last year, with a 6.1% increase taking the average price to £332,088.
In two areas - Wales and the North East of England - sellers' asking prices are lower than a year ago. In Wales, asking prices fell by 1.1% annually to reach £164,291. In the North East of England, they fell by 1.7%, taking the average asking price to £139,527.
Rightmove also quoted the views of estate agents.
Kevin Shaw, national sales director at estate agency Leaders, said: "It is clear that first-time buyers are outnumbering buy-to-let investors right now. We have seen an increasing number of one-bedroom apartments, which historically would attract first-time buyers and investors in equal numbers, snapped up by the former.
"This is largely because first-time buyers have had numerous offers accepted over the asking price so are obviously determined and able to secure these properties in the current market. Investors are understandably focused on the price as this drives the yield and generally do not want to get into a bidding war to secure these properties."
Mark Manning, director of Manning Stainton in Leeds, Harrogate, Wetherby and Wakefield said: "New seller inquiries are 26% up on the same time last year giving the strongest indication that we may see a slight ease in the lack of supply in the market.
"Now, this will be welcome news amongst first-time buyers who have registered in strong numbers and are waiting for much-needed new stock to come to market.
"Combine this with a comparative reduction in new investors and landlords of 32% over the last quarter compared to the same quarter a year ago and this may well be the year of the first-time buyer."