Phoenix has launched a mandatory bid for Hornby, after offering to buy a stake from another investor that would gave it a 55% holding in the firm.
The offer, of 32.375p per share, values Hornby - which also owns the Scalextric and Airfix brands - at £27.4m.
Hornby has advised investors to take "no action for the time being".
The toymaker also said it had appointed David Adams as its interim chairman, replacing Roger Canham who resigned from Hornby's board on Wednesday. Mr Canham is also the non-executive chairman of Phoenix Asset Management.
On Wednesday, Hornby had reported falling revenues and deepening annual losses.
The company is struggling to revive its fortunes, which has led to it cut back the number of products it sells.
In the year to 31 March, revenues fell to £47.4m from £55.8m, while underlying losses widened to £6.3m from a £5.7m deficit last year.

The Ireland front row was suspended for two games by European Champions Cup organisers following an incident in the defeat by Toulon in France last Sunday.
Leinster have appealed, arguing that Healy was cited for one offence yet suspended for another.
As the appeal cannot be heard until after Saturday, he is free to play.
The 28-year-old could still miss the Pro12 meeting with Munster at Thomond Park on Sunday, 27 December.
"Leinster believe this is a failure to follow due process and is unfair to Cian Healy," the Irish province said.
Healy was handed the ban for dangerous play after being charged with striking Toulon hooker Guilhem Guirado with his knee during the 24-9 defeat in France.
The striking charge was found to be not proven but the incident was deemed to be foul play.
"As a written decision of the judicial officer is not available, it has not yet been possible to hear the player's appeal nor set a date for the appeal," said organisers European Professional Club Rugby.
"The player is therefore free to play until the outcome of his appeal."

The club's fans have previously booed to express anger at European football's governing body over a number of issues.
Uefa opened disciplinary actions against City in October 2015, but decided against any sanctions.
The new 2017 disciplinary regulations contain no reference to causing a disturbance during competition anthems.

Forecasts were predicting a 4.1% fall in exports, but a weakening currency may have boosted the lagging sector.
Imports also beat expectations in yuan-dominated terms to only fall 4%, compared to forecasts of a 7.9% slump.
The jump in exports was the first rise since June last year as the sector has been battered by slowing demand and slumping commodity prices.
For the year, exports fell 1.8%, while imports tumbled 13.2% from 2014.
China's customs spokesman Huang Songping said at a news conference in Beijing that the country's exports fell last year due to weak external demand.
Trade figures in US dollar-denominated terms came out later in the day and were also better-than-expected. Exports fell 1.4%, compared to forecasts of an 8% fall, while imports declined 7.6% against expectations of an 11.5% decline.
The country's central bank had been aggressively weakening the yuan guidance rate -the rate the bank fixes for the currency on a daily basis - last week in an attempt to boost the sector.
But the depreciation of the yuan sparked fears that other countries in the region would also start to devalue their currencies to compete with China on exports and that rattled global markets.
This week, it has set the yuan rate steady in attempt to calm volatility in equity markets and soothe fears that China's economy may be slowing faster than anticipated.
The world's second largest economy is already expected to have grown at its slowest pace in a quarter of a century last year, with Beijing targeting 7% growth.
But many economists have warned that the Asian giant may undershoot that target as key sectors such as exports, manufacturing, property and consumption struggle to gain momentum.
However, Wednesday's closely watched better-than-expected figures could go a long way to ease fears about the Chinese economy at a time when attention is focused on how authorities are handling the market volatility.
The benchmark Shanghai Composite index was up 0.7% to 3,044.52 after the data was released.
Model toymaker Hornby has said a takeover offer from its largest shareholder, Phoenix Asset Management, "significantly undervalues" the firm.
[NEXT_CONCEPT]
Leinster prop Cian Healy is available for Saturday's game with Toulon after it was ruled he can play until his appeal against a two-game ban is heard.
[NEXT_CONCEPT]
Manchester City will not face punishment from Uefa this season if their fans boo the Champions League anthem after a change to regulations.
[NEXT_CONCEPT]
Chinese exports defied expectations in December to rise 2.3% from a year ago in yuan-denominated terms.