Bale, 26, has not played since injuring his calf in Real Madrid's 5-1 win against Sporting Gijon on 17 January.
Liverpool expect Allen, 25, to be out "for a while" with a hamstring injury.
Wales assistant manager Osian Roberts is "hopeful" Bale will be fit but said: "The most important thing is the injury clears up because it can re-occur."
Bale is expected to miss Real's Champions League game against Roma on Wednesday after suffering a minor setback in his recovery.
"Time will tell over the next two or three weeks how that develops as Gareth steps up his rehab, and we'll take it from there," added Roberts.
"He's got some key games coming up for Real Madrid and it's important for us that he's fully fit for such an important tournament in the summer.
"Both ourselves and his club will have Gareth's best interests at heart. It's important that the injury fully heals and he doesn't come back too early."
Wales host Northern Ireland at Cardiff City Stadium on Thursday 24 March before facing Ukraine in Kiev four days later as part of their preparations for Euro 2016.
Allen is likely to miss Liverpool's League Cup final against Manchester City on Sunday 28 February after his penalty against Stoke in the semi-final shootout secured their place at Wembley.
"Joe has been unlucky with injuries. As far as the friendlies are concerned it's going to be tight. Time will tell," said Roberts.
"There's no need to rush him back. We know what Joe can do.
"The important thing is that the injury is fully healed and he can have a run of games before the end of the season."
Roberts was speaking at a Football Association of Wales grassroots coaching conference at Dragon Park in Newport.

The EC135 helicopter pilot was forced to manoeuvre to the right during the incident over Perthshire on 25 March.
The pilot was returning to base at Perth Airport after dropping off a patient in Glasgow.
A UK Airprox Board (UKAB) report said that the two aircraft came within 200m of each other.
The report said that the motor-glider had been invisible to the pilot due to being obscured by the windscreen pillar.
The pilot of the glider has not been traced.
The report noted that "flight crew situational awareness" was assessed as "ineffective" because there was no information available to the pilot to warn him about the motor-glider.
It said that as the pilot was operating in Class G or uncontrolled airspace without a collision warning system.
As a consequence "see and avoid" was his "only mitigation against mid-air collision".
The report said: "The fact that he was conducting his arrival checks had understandably reduced his and his crewman's capacity for robust and effective look-out.
"That being said, although it was a late sighting, he did see the other aircraft in time to take avoiding action, albeit achieving less separation than would be desirable."
The charity leases the EC135 helicopter and pilots from Babcock Mission Critical Services (Onshore) Ltd.
Scotland's Charity Air Ambulance chief executive David Craig said: "We are currently reviewing the report and the observations and recommendations contained within it.
"I am meeting with our aviation providers Babcock Mission Critical Services (Onshore) Ltd. later this week to determine what steps, if any, we should be taking in response to this incident and the report findings."
Wales are unsure if forward Gareth Bale and midfielder Joe Allen will be fit for their friendly matches against Northern Ireland and Ukraine in March.
[NEXT_CONCEPT]
Scotland's Charity Air Ambulance had to take evasive action to avoid a collision with a glider, a report has revealed.